The former Manchester United team-mates clashed at Eastlands on Tuesday as Tevez celebrated his equalising goal in City's 2-1 Carling Cup win.
Tevez initially made a "shut it'' gesture in response to pre-match comments from Neville that the Argentina star was not worth the money it would have cost United to keep him at Old Trafford last summer.
Neville responded with a one-fingered gesture of his own, which prompted further reaction from Tevez, who followed up by winning the game with a second-half header and then aimed fierce criticism at the Red Devils skipper.
In a wide-ranging attack, Tevez labelled Neville "a moron'' and "a boot-licker'', which has only served to add further fuel to the fire ahead of next Wednesday's semi-final second leg at Old Trafford.
Although he has never been scared of courting controversy, United manager Ferguson has this time opted to give the whole row a wide berth.
"I am not interested,'' he said. "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.''
Ferguson also declined to offer an opinion on Neville's behaviour, which it has now been confirmed will not attract any further action from the Football Association, claiming he had not seen what happened.
"I am not disappointed with Gary's conduct,'' he said, "and I didn't see his gesture.''
United defender Jonny Evans is not convinced Neville actually said what Tevez accused him of.
"Gary and Carlos are not team-mates any more and they don't have to be pals but I think this has all been lost in translation a little bit,'' Evans said. "I don't think Gary said Carlos wasn't worth £25 million. He was just saying the manager usually gets these decisions right and we will get on with it. From what I hear, either Carlos has read it wrong or someone is winding him up and he has reacted."
City manager Mancini has told Tevez not to make any further remarks about about his former team-mate. Regarding Tevez's outburst, Mancini said: "I think these things can sometimes happen after a match. The players are tired and sometimes they do not think what they are saying. It is important that this matter is finished now as we need to focus on our next game.''
Mancini confirmed Tevez will be rested for the FA Cup match against Scunthorpe on Sunday, so he is fresh for the second leg at Old Trafford on Wednesday. The Italian boss does not believe Tevez's comments about Neville could provoke crowd trouble.
He added: "I hope not. In England it is beautiful as families go to a match. People have the right attitude.''
Meanwhile Mancini expects Emmanuel Adebayor to return to the club on Sunday. He has been on leave in Togo following the machine-gun attack on the national team coach before the African Nations Cup that left three people dead.