City wanted the Dutchman in the summer but the then Arsenal forward preferred to join United, snubbing the opportunity to play for the champions.
"At this moment Robin van Persie is a very important player for United. He has scored 13 or 14 goals and it is clear he has changed their situation. At the moment, he is the difference between us," Mancini said.
"We were very close to signing him, I know what the reason was but I won't say. It was not about money. We wanted Van Persie because we knew he was totally different from our other strikers.
"We wanted to improve our team, particularly for the Champions League. We were very close and we were sure it would be very good for us but it didn't happen and now we can do nothing about it. We were very close three or four months before he went to United."