"It is finished now," Italian Mancini told a news conference on Friday.
"It is important that the players now think of the next game."
Asked if the spat could cause problems between the two sets of fans Mancini said: "I don't think so.
"In England it is beautiful because the supporters go to watch a game and a match and only for this. I don't think the people are very serious so there will be no problems."
Tevez, who scored both goals in City's 2-1 League Cup semi-final first leg win over Manchester United on Tuesday, called defender Neville a "moron" and accused him of sucking up to his manager Alex Ferguson in an interview in Spanish with Argentina's Radio Rivadavia.
He was responding to questions about a gesture he made to Neville - indicating the United player talked too much - after scoring his first goal.
Neville had angered Tevez by repeating comments made previously by Ferguson that the Argentine was not worth the fee United would have been forced to pay to keep him last year.
Tevez cost City around 25 million pounds when he joined in July.
The second leg of the semi-final is at Old Trafford next Wednesday.
NEWS: Tevez slams 'suck-up' Neville
