The Belgium international picked up the problem in the Premier League champions' draw with Real Madrid last week and was struggling to recover before the clash at Stamford Bridge.
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But after being declared as fit to play, Kompany produced a superb performance, and was delighted to keep a clean sheet against the Blues' fearsome front line.
"I was on crutches just 48 hours ago," he told City's official website.
"I wanted to play for the team. I had said that I wouldn't play if I couldn't give everything I had on the pitch. But I am happy I was able to take part, because it was not the most comfortable game.
"It's always a difficult away game. I don't think there are many times we come here and win.
"In the end it was a draw and as a defender I am happy with a clean sheet - I guess that's what I'm going to take out of the game."