City prevailed at the Etihad Stadium 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.
The managers had to be kept apart on the touchline by fourth official Mike Jones after a difference of opinion over Nigel de Jong's foul on Danny Welbeck led to angry words and gestures being exchanged, although the pair did shake hands at the final whistle.
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 [Monday], 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."
United boss Sir Alex Ferguson felt his side were poor on the night and conceded the title was now City's to throw away.
"It was feisty, competitive, not a lot of goal chances," the Scot said. "We're disappointed we never tested their goalkeeper.
"They had more threat as they had more action around the edge of our box."
Ferguson was also left to lament the manner of City's goal, which came from a corner right on the stroke of half-time.
"If you lose a goal from a set-piece at this level, you only have yourself to blame for that," he said.
"It was a bad time to lose a goal."
He added: "I think they're in the driver's seat now. They've got to win two games of football.
"It's not over yet, but they've got an eight-goal advantage. It's a big advantage."