Mistakes in defence cost Manuel Pellegrini's side as Villa came from 2-1 down to claim all three points in the Premier League clash..
"We felt confident we were going to win the game but three chances, three goals - I think that sums the game up. We could have scored five or six," defender Kompany told reporters. "We have to pick ourselves up and make sure next game we don't make the mistakes and hope to be a bit more lucky.
"The first [Villa] goal was offside and the second goal, a free kick, is never really something you can do about. We have lost games before, every team in the world has lost games.
"It is about the reaction, what you do next game. If anything I think we will be more motivated now to make it right."
City face Bayern Munich in the Champions League on Wednesday.