City were 2-1 ahead in the second half but conceded twice in five minutes to lose the Premier League encounter at Villa Park.
"If we played that game 10 times, we would win nine of them," Kompany told BBC Sport. "It was a very unlucky result and a very unlucky day.
"Villa had three chances and scored three goals and that was it. The first goal was offside and we did not get the decision - but every time we made a mistake, we conceded."
City are now fifth in the Premier League after six matches.