Kilmarnock's Kyle Vassell and Brad Lyons look dejected after Copenhagen's goal
Derek McInnes said he is "immensely proud" of his Kilmarnock players, despite them falling short of upsetting Copenhagen as the Danes snatched a draw at Rugby Park to end the Ayrshire side's European journey.
A Marley Watkins first-half strike put buoyant Kilmarnock just one goal behind on aggregate, but they were unable to capitalise on any dominance and soon saw their dreams dashed in the second half by a Lewis Mayo own goal.
Although the hosts played well for large spells, they relied on two wonderful saves from Kieran O'Hara to keep them ahead in the first half and saw Denis Vavro hit a post from distance.
"We said to the players prior to the game, regardless of the outcome, we were immensely proud," McInnes told BBC Scotland.
"I tried to give them real belief pre-match. We felt the harshness of last week, but we were a match for them and we tried to take that confidence into the game.
"We knew we had to plant a seed of doubt and we did exactly that. We were terrific from the get go. We sensed a second goal.
"That said, they had a couple of moments on transitions and we knew that's where we would be vulnerable."
Attention now turns to the league, where Kilmarnock sit bottom of the Scottish Premiership after losing their three games so far.
Going in as underdogs and 2-0 down, Kilmarnock started with no fear and look to have rattled their Danish opposition.
However, it was Copenhagen who should have opened the scoring. Elias Achouri set up 18-year-old Victor Froholdt, who somehow put wide from six yards out.
Kilmarnock punished them for that miss. A long-free kick was nodded on to a post by Stuart Findlay, Joe Wright hooked the rebound at goal, but somehow Nathan Trott kept it out.
The goalkeeper couldn't stop Watkins' rebound though, and the roof came off Rugby Park.
The goal lit a spark under Copenhagen, who immediately set about getting a leveller. Viktor Claesson was denied by a world-class save from O'Hara, before Vavro's effort kissed the woodwork.
With seconds ticking down the break, the visitors had one more chance when Kevin Diks was picked out at the back post, but his lightning-quick volley was also saved by O'Hara.
Those stops meant Kilmarnock went in at the break 1-0 up and, despite being under pressure, the momentum was behind them. That would be the best of it.
The second-half was a different affair, trying to stem Copenhagen attack after attack. There was just one home chance - a shot from Vassell that Trott saved.
Eventually, the dam burst. Achouri controlled a long diagonal ball and fired a cross towards Orri Oskarsson, but it was turned into his own net by Mayo before it could find the Icelandic striker.
Suddenly two goals behind again, Kilmarnock's task became insurmountable.
It almost got worse, but Mohamed Elyounoussi's header rattled the crossbar rather than rippling the net.
Brave Kilmarnock run out of steam
Boss McInnes said he wanted this game to become a "nightmare" for Copenhagen and, for a while it was.
They pressed their opponents high from the first whistle, making the game really uncomfortable for the Danes, who started to look nervy.
They got their reward for it - unsurprisingly from a set-piece - but the cracks started to show after the break.
They couldn't keep that relentless energy up and stepped a yard off Copenhagen, who took full advantage of the extra time and space to click into gear, playing the game they wanted it to be played.
It's been far from the dream start to the season for Kilmarnock. They've struggled for fitness and had to rotate heavily because of the demand of European games.
However, they can leave Europe with their heads held high after a few battling performances. They need to show that grit in the league now - just like they did last season.
What they said
Kilmarnock manager Derek McInnes tells BBC Scotland: "I thought Kieran O'Hara was terrific, some fantastic saves. Half-time came at a bad time for us.
"We gave ourselves a chance tonight, that's the thing. We could have set up and been a bit more canny in our work. I don't think they enjoyed the game.
"At the start of the second half, they enjoyed the game too much for my liking. We needed to take the sting out of the game. Their movement was good.
"Over the piece, we had a proper opportunity. The own goal was harsh on us but the game played out in a manner which I hoped. We just never got the second goal."
