City are unbeaten this season and Mancini was pleased to get the better of a side he has a lot of respect for.
"I am happy. We didn't play very well in the first half, we know Wigan are a good team," he said.
On his changes, he added: "Wigan play with three defenders and two in the channels. I wanted to put players in the same positions as them and when we changed it, we scored the first goal. After that, the match changed.
"When we have played against Wigan it has been a difficult match because they play very well."