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The Brazilian goalkeeper produced another superb individual display at Turf Moor, making a number of crucial saves, not least a remarkable second-half block from Aaron Lennon.
"I think that you judge a good goalkeeper not by the amount of saves he makes but the importance of the ones he saves," said Kompany.
"Today there were a couple of chances where we lost the second ball for some reason and to have him make the save just shows what a tremendous player he is to have in your squad."
It was only the third time the opposition have held City to a draw in the league, with Johann Berg Gudmundsson's second-half goal cancelling out Danilo's superb first-half opener.
City created numerous chances with Raheem Sterling missing the best opportunity in front of goal shortly before Burnley's equaliser.
And though City are now 16 points clear at the top of the Premier League, Kompany said it was a valuable reminder to the Blues of the need to be clinical.
"We never doubted this league was competitive. We were warned for this kind of situation and we knew we would have to take our chances," Vincent added.
"We created some chances in an incredible manner but we probably ran out of steam a little bit. We kept trying and trying but in the end we were punished and we mustn't feel too sad about this as our performance was good.
"Raheem has been incredible for us and he's probably scored more last-minute goals than anyone but today it just didn’t quite happen.
"We have to make sure we finish games a little earlier next time but If we keep playing like we do we will win more games than not."
It was the Belgian central defender's first league appearance since he was forced off through injury away at Newcastle in late December.
And the 31-year-old admitted he was delighted to have got 90 minutes under his belt.
"I enjoy every minute be it playing or training. I'm looking forward to the next game in what is an amazing season.
"It has been challenging but at the same time one of the best experiences so far with the amount of special games we've been involved in."
We hear from the boss after the draw at Turf Moor
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Match report of Burnley v Manchester City...