Kompany must now reinvigorate his team-mates ahead of next month's trip to Barcelona but he is still upbeat about their chances of progression.
The Belgium international told ITV1: "By no means we thought they were superior. When it was 11 v 11, maybe we showed a bit more respect.
"There was a lot of soft fouls. In the Premier League they would have not been given.
"If the tempo was in this game it would have been to our advantage.
"If the game is the same as today, and we manage to stay away from some fouls, we have got a chance [in the second leg]."