"These things sometimes happen after a game. Players are tired and don't think what they're saying," said Mancini.
Greater Manchester police have also urged for calm between rival fans.
Mancini added that "it is important the matter is finished", while the police are hopeful that is the case and that it does provoke antagonism between the sets of supporters.
The atmosphere is likely to buoyant at Old Trafford for Wednesday's semi-final second leg as United try to overturn a 2-1 deficit.
And Greater Manchester Police assistant chief constable Ian Hopkins has called for fans to be on their best behaviour.
He said: "As one of the host cities for the 2018 World Cup bid, the second leg truly is a great day for Manchester to shine. We would ask that fans play their part by behaving sensibly and do the city proud.
"I would like to stress that although the rivalry has always been there between the fans, previous derby matches have passed off largely peacefully and without major incident.
"I would ask that fans adhere to this tradition on Wednesday, regardless of what happened in the first leg."
Before the first-leg tie at Eastlands, Neville said United manager Sir Alex Ferguson had been right to let Tevez leave the club last summer, rather than signing him on a permanent deal after his two-year loan spell ended.
I was honourable at all times and I think it was wrong of him to talk about another footballer in that way Tevez on Neville Tevez scored twice in City's 2-1 win, and gestured and cupped his ears after scoring his second goal.
Cameras appeared to catch Neville making an obscene gesture in response, and afterwards Tevez said his celebration had not been aimed at the United bench but specifically at his former team-mate.
"My celebration was directed at Gary Neville," Tevez told ESPN Argentina.
"He acted like a complete boot-licker when he said I wasn't worth £25m, just to suck up to the manager.
"I don't know what the hell that moron [tarado] is talking about me for. I never said anything about him.
"I didn't go overboard in my celebration and it was directed at Gary, not at Ferguson and not at the fans.
"I think he did the wrong thing because I was his team-mate and I never said anything bad about him."
The row has made plenty of headlines and has done little to help the Football Association's hopes of reducing tensions between the clubs ahead of the second leg at Old Trafford on 27 January.
But Ferguson did his best to play down the significance of the row when asked about it at his news conference ahead of Saturday's game against Hull.
"I am not interested," said Ferguson.
"Carlos Tevez is not our player anymore and I have nothing to say about it at all.
"Players argue with each other all the time. They have a go at each other time and time again. It is not an issue for us. We move on."
Two wrongs don't make it right. They were both incorrect and set no example to kids pogmonthoin The fierce rivalry between the teams has taken on a new dimension since the arrival of City's ambitious new owners, who have spent large sums to help the club join the elite.
Since joining City on a five-year deal, accusations have flown back and forth between Tevez and United over the circumstances of his Old Trafford exit.
His radio interview was far stronger than the comments Thursday's newspapers carried from the Argentine via his representatives.
"I thought Gary Neville had been disrespectful by talking about me like that," Tevez said.
"He cannot possibly know the full story of what happened at Old Trafford. I was honourable at all times and I think it was wrong of him to talk about another footballer in that way.
"For me, to celebrate in front of him was not malicious. It was just banter. That is what the game is all about. I didn't see if he did anything back."
Neville looks likely to escape punishment for the Tevez incident, as it would be difficult for the FA to prove his gesture was particularly aimed at the Argentina international, but he has been warned over his behaviour before.
Last September, the England defender, 34, was cautioned about his future conduct following United's dramatic 4-3 win over City when he ran towards City fans to celebrate Michael Owen's injury-time winner at Old Trafford.
And in 2006 he was fined £5,000 and again warned over his future conduct after celebrating in front of Liverpool's fans after United secured a late winner over their other main rivals.
In the radio interview, Tevez also revealed he finds living in England challenging.
"The truth is that it's very, very hard for me to live here, so far away from my loved ones," said Tevez.
"I'm not exactly an example of how to learn English; I just can't get it into my head. I'm learning hardly anything, truth be told. I don't go out much, I spend most of my time at home."