City prevailed 1-0 thanks to captain Vincent Kompany's first-half header to take them top of the Barclays Premier League table, above United on goal difference with two games each left to play.
Ferguson said: "He was badgering the referee the whole game, the fourth official and the linesman, and the minute I go out there...
"He was complaining about referees all week, he can't be complaining tonight, that's for sure."
Victorious Mancini played the incident down, adding: "I don't remember (what the row was about). I told the fourth official it was a foul for us, not against.
"At that moment the tension was high, but for me it's forgotten."