City managed to pull clear of the Latics late in the second half thanks to a trio of goals from Carlos Tevez which put them just two points in arrears of Tottneham in fourth place and Mancini was relieved with the three points.
"It was an important win, it wasn't easy and it was difficult in the first half because Wigan played very well and there was no tempo from us," he told ESPN.
"We played better in the second half and after the sending off it was too easy. The sending off probably changed the game."
"Carlos is a fantastic striker and I hope he continues (scoring) in the last seven games," Mancini added.
"I also hope Emmanuel Adebayor can play better. He's been out of the game for a long time (four-match suspension) and it's difficult in the first game when you come back."