The home side started well, Halilovic's low corner into the box sliced over the bar by Puncec from 12 yards out just two minutes in. Moments later Shay Logan blocked a ferocious shot from Acosty, needing a few seconds afterwards to clear his head.
The Dons carved out their first opening after nine minutes. A fine free-kick in from Niall McGinn some 35 yards out picked out Sam Cosgrove. His towering header down came tantalisingly close to Lewis Ferguson in front of goal but Acosty was just in front of him and able to scramble the ball clear.
Rijeka had good possession for the first time around the quarter hour, the lively looking Acosty causing problems before the ball broke to Colak 25 yards out, his shot always bending well wide.
A thunderous shoulder first challenge on Ferguson from Capan somehow didn't draw a card from the referee after 18 minutes, the youngster getting slowly to his feet thereafter. Ryan Hedges then took an even heavier blow, albeit accidental, in a mid-air collision that needed some treatment before he was able to continue midway through the first half.
The best effort of the game thus far came in the 27th minute, again for the home side, Acosty working the ball into Halilovic, his effort from just outside the box swerving as it flew over the bar, Joe Lewis always having it under control.
Two minutes later came a better chance still, a cleverly worked corner in from Halilovic allowing Lepinjica to fire a first time effort goalwards, Lewis down to his right to produce a brilliant reflex save. The ball rebounded out to Zuparic on the edge of the six yard box but with all the goal to aim at, he somehow scuffed his shot wide for a real let off.
On 33 minutes, good work from Leigh and Jon Gallagher set McGinn running across the top of the box only to be brought down though remarkably, no foul was given.
From there, the home side began to enjoy a spell of good possession, the Dons keeping a good shape to keep them at arm's length, the only criticism being that when Aberdeen did win the ball back, they were a little lax in their use of it. That said, the Dons began to push the tide back in the last few moments of the half to see themselves safely through to the break with the clean sheet still intact.
HALF-TIME: HNK Rijeka 0 Aberdeen 0
Early signs that Rijeka's patience was running out against Aberdeen's strong defensive shape came in the first minute of the second half, Lepinjica firing hopefully at goal from all of 35 yards, never troubling Lewis.
They were more impressive in the 49th minute, clever play down their right creating space for Halilovic to drift inside and drive a left foot shot that didn't flash too far past the far post.
The referee finally produced a card in the 54th minute when the pace of Gallagher forced Kvrzic into a lunging tackle on halfway. From the resultant free-kick, the Dons eventually created space for McGinn to curl in a cross that was just a shade too strong for Andrew Considine. With the home crowd getting frustrated, Aberdeen began to ask more questions, Ferguson playing further forward than in the first 45 minutes.
Frustratingly, having done all the hard work, from nowhere Rijeka were gifted a penalty, Logan penalised for the slightest tug on Colak's shirt, Logan also collecting a booking after the striker's theatrical fall, one of many across the evening. Colak picked himself up and smacked his penalty kick straight down the middle to make it 1-0 after 62 minutes.
Acosty made way for Muric before the restart and Zuparic was then almost immediately booked for a horrible studs up challenge on Gallagher and, from the free-kick, McGinn's ball flashed through the box and just wide of the far post, Considine again the closest Aberdeen player to the ball.
Another inswinging corner from Halilovic caused havoc in the Aberdeen area in the 73rd minute, the ball flashing through the area without drawing a finishing touch as the hosts were now playing with renewed confidence after the goal.
With 15 minutes to go there was a slew of changes, McGinn and Gallagher making way for Dean Campbell and Scott Wright for Aberdeen, Tomecak replaced by Raspopovic for the home side. Four minutes later, Capan became the third Rijeka name to go into the book.
Frustration was creeping into the Dons' game by this stage, Cosgrove trying a very ambitious shot from 30 yards with eight minutes to go that was easy for Prskalo in the Rijeka goal. Iglesias then replaced Capan in the 84th minute as the Croatians made their final change. Derek McInnes took his last throw of the dice two minutes later, Curtis Main replacing Hedges as Aberdeen went after the away goal that would change the complexion of the tie.
But it was Rijeka who got the crucial goal with three minutes to go, Muric showing great control to get himself away from Campbell before drilling in a vicious shot from the edge of the box that buried itself in the bottom corner.
Cosgrove found his way into the referee's book as the game entered three minutes of added time and Ferguson almost pulled a goal back moments later, a 25 yard drive getting a deflection that was well handled by Prskalo, but it really wasn't the Dons' night.
A harsh scoreline in the end from a game where there wasn't much between the sides, but it leaves the Dons with a lot of work to do in the second leg at Pittodrie. Then again, Aberdeen did beat Rijeka 3-0 the last time we met in this competition.
"So it all seemed very unnecessary for me. Whether it is a penalty or not, I can't be certain. It certainly was not a dangerous situation.
"It just compounds the disappointment.
"I thought at that stage, 62 minutes in, I thought they were huffing and puffing. I though their crowd were maybe getting a little bit restless. And the game was quite uneventful for me and that was suiting us. I felt very comfortable, Joe only had one save to make up to that point, in the first half.
"The penalty seemed to be a bit of a gift for them."
"It is clearly not an ideal scoreline to be taking back to Aberdeen.
"But if the roles were reversed, if we had won the first leg at Pittodrie 2-0, I would still think there was work to do.
"I still think the tie is alive.
"It is far more difficult than it was from the outset, but we have shown already at Pittodrie this season at home that we have brought big performances.
"We have showed plenty of quality and it will need that and more against a better opponent. They are clearly a good side. I said that before the game - and I meant it with the greatest of respect. Compared with the previous Rijeka team we played, this one has more athleticism, more physicality about them.
"I think the changes their manager made tonight, bringing two more powerful players into the team to play us maybe suggests that.
"I feel that a lot of things need to go our way next week.
"Although we are down and we are disappointed, we don't feel that we are out of the tie.
"We take encouragement from previous home performances this season.
"We know that if we can get an early goal then it is game on.
"Clearly they are in the box seat and in charge of the fixture, but we still have the opportunity to change that."
More of an attacking threat
"You have always got to get the balance right between attacking and defending.
"If you don't give away the cheap penalty, you would say a lot of the work was right tonight.
"And I still think we did a lot of good work.
"I thought my back four were fantastic tonight. I thought McKenna and Considine really dealt with a good striker for the vast majority of the game. We showed the defensive qualities of the team for the vast majority of the game.
"You cannot be too open or too expansive away from home.
"We maybe get an opportunity to show more of an attacking threat next week and we know, as we have shown already this season, if we can find that quality and verve to our attacking play then we will cause them problems."
"We had the team meeting at the hotel. Scott McKenna has his game head on. It was probably a bit of a relief and release for him to concentrate on the game. His performance tonight shows clearly why there is interest in him. It is why myself and everyone thinks so highly of him.
"His performance, he was on it tonight.
"He was really focussed and that is a testament to him.
"He has been through the ringer the last little while. And he has had a lot to contend with. He has had a lot of people in his ear and he has had a lot to consider and no shortage of disappointment probably.
"But he channelled it the right way.
"McKenna is only going one way.
"He is only going to the top for me.
"He showed tonight how important he is for us and while he is still an Aberdeen player he will keep delivering those types of performances, the type of performances he has put in since he came into the team.
"I was told there was a phone call from one other Championship club but it was not an offer. It was just an indication that they might put in an offer but it would have been too late today. We had a game to prepare for. When he woke up today he was not going anywhere."
"Zak coming in gives us another defender in the building. We only had six senior defenders and we had three of them injured at the one time.
"I have said often enough that I have always liked a couple of centre defenders in my squad who can play full back. Andy can do it, Zak can do it.
"He gives us competition, he gives us a bit more flexibility, he gives us good options, but he is also a good size. He uses the ball well and he has good pace. I think he will prove his worth to us. I am delighted to get him in.
"I am grateful to the club that we have been able to bring him in."
"Michael deserves so much credit. He has pushed and pushed to get on that plane despite only having on training session under his belt.
"The way things were playing out over the last 48 hours, we might have needed him.
"It is testament to him that he has managed to get here and be available.
"And the same with Zak, who had a bit of a journey to get here this afternoon. He showed his determination to get here as well and thankfully so.
"It is good to have more options, especially with the game coming up on Sunday."