The Dutch visitors opened up a two-goal advantage in the early stages, with both goals coming from set pieces.
Kompany believes that despite defending poorly from corners, City fully merited a victory thanks to their second-half response.
He told Sky Sports News: "It is very disappointing because I am sure we did enough to win the game.
"At corners, it is important to defend as a team and we probably let ourselves down, especially because they didn't have a lot of other chances.
"We will try to see what went wrong but it's not a case of us not being good enough. I don't know about the penalty at the end but I am sure we should have had a penalty in the half as well (when Yaya Toure was fouled). It was very clear."
City's Champions League hopes are alive by the slimmest of margins, with the reigning Premier League champions rooted to the bottom of Group D.