City dominated for much of the afternoon but they twice surrendered a lead as Villa exploited defensive frailties to claim a 3-2 win.
Kompany said: "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.
"We have to pick ourselves up and make sure next game we don't make the (same) 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."
The result left City still without an away win in the Premier League this season after defeat at Cardiff last month and a goalless draw at Stoke.
Kompany said: "I would be more worried if it was a case of being dominated, of not creating enough chances. I don't think that was the case."