The France international, signed from Porto during on deadline day, scored an own goal and gave away a first-half penalty at the KC Stadium on Saturday as the visitors surrendered a two-goal advantage.
Manuel Pellegrini's side fought back from the disappointment to win 4-2 and end a three-game winless streak in the Premier League.
Having single-handedly gifted Hull a way back into the game, Kompany was impressed with Mangala's attitude to ensure the defending champions sealed all three points.
"As defenders, we have to deal with this, it's part of the job," said the City captain. "I always look at the reaction and we saw it from him in the second half.
"It could have been so dangerous because it had gone two-all, you’ve got time to think about it in the dressing room, but he just got on with it and stood up to the task.
"The rest of the game, he played well, he stayed professional.
"You could not have asked for more. The main thing is to stick to your job, sometimes you get a half an hour like this.
"I've seen in him a great reaction and in the second half he was spot on."
The victory took City up to third in the league table after six matches, with unbeaten Chelsea five points ahead of them at the summit.
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