The Sky Blues conceded twice early on from set-pieces, but were able to fight back to earn a draw at the Etihad Stadium.
After the game the Belgian confessed that the goals they shipped were avoidable and cost them their chance to win:
“It’s very important to defend as a team when corners come in and we’ve probably let ourselves down on those two occasions.” He told ITV after the game.
“Those two goals were really not good.
“We’ll look back at the game, try to see what went wrong, and try to improve.”
“It’s not the case that we’re not good enough for the Champions League but it’s a matter of time.
“It’s unfortunate that we’re letting those chances go at the moment.”
City were denied a penalty late on in the game as Mario Balotelli appeared to be wrestled to the ground in the area.
Both the striker and manager Roberto Mancini were angered by the decision not to award a spot-kick, but Kompany refused to blame the officials:
“You guys have the images and you’ll be able to judge better than me.” He responded when asked if it was a foul.
“We didn’t do enough to win tonight and we have to learn from this and take it into the next game.”
Ajax took the lead after ten minutes, as Siem de Jong poked home from close range. The Dutchman then doubled the lead with a header following some slack marking from the City defence.
The home side battled back with goals from Yaya Toure and Sergio Aguero, but were unable to force a winner leaving them rooted to the foot of Group D.