The Eastlands outfit crashed out of Europe's premier club competition at the Round of 16 phase 4-1 on aggregate to the Catalan giants after Lionel Messi and Dani Alves scored either side of Kompany's late goal at the Camp Nou.
Pablo Zabaleta was sent off in the 78th minute for a second yellow card when arguing what should have been a penalty to Edin Dzeko which made life difficult for the visitors, just as it did when Martin Demichelis was shown a red card in the first leg.
City began slowly before producing a number of chances in the second half but in the end it wasn't to be as Kompany was left to ponder what might have been.
"I think I speak for the team in saying we've got nothing left in the tank," he told Sky Sports.
"We gave everything. A few times we could have scored, and obviously that would have changed the game.
"Going for a second time down to 10 men after it was a clear penalty, it's not easy conditions to come and play against a strong team.
"Over the course of two games, it's funny I say this, but whenever there was 11 players (against 11) there wasn't much between the two teams.
"Obviously, Messi is an incredible player and whenever he has the ball danger can happen - but outside of that we had huge changes. If we score, we're looking at a completely different game."
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