After underlining their Barclays Premier League title credentials with a magnificent 4-1 defeat of Manchester United last week, City were expected to win with ease at Villa Park.
For much of the first half it seemed that would be the case as City dominated but they twice surrendered a lead after the break and Villa snatched an unexpected 3-2 win.
Manager Manuel Pellegrini described the outcome as "unbelievable" after the game and Kompany seemed similarly baffled, but is determined to ensure it is not repeated.
The influential defender 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 first half was a one-sided affair with City, even without matching the intensity they showed against United, piling on the pressure.