The Premier League side were undone by Martin Demichelis’ sending off early in the second half for a foul on Lionel Messi which gave the Argentina forward the chance to open the scoring from the penalty spot.
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"It’s very tough," he told ITV. "By no means did we feel they were superior to us. When it was 11 vs 11 we showed them too much respect. They were there for the taking. They were not the best team we have played this season, not at all.
"They were incredibly efficient and when you play against them you do realise the individual quality of this team is phenomenal. It just makes it so difficult to close them down.
"It's not the team that's put in the best performance against us but it doesn't mean it's not the best team. If they turn up at Camp Nou in the next game and play like they're capable of playing then it's a very tough game. If the game is the same as today and we manage to keep away from small fouls we've got a chance."
City had competed well with the Spanish champions up until the moment Demichelis brought his compatriot down, marginally outside the penatly area, but once Messi converted from 12 yards the game and indeed the tie adopted a completely different complexion.
Kompany added: "I don't know [if it was a penalty]. I've not seen it. There were a lot of soft fouls today, in the Premier League there would have never any of those fouls given. Normal challenges when you take the ball and it's a foul. I thought that if the tempo had been in this game it would've been to our advantage."