The striker claimed Mancini was in a foul mood and swore at him as he sat on the bench during the Champions League defeat at Bayern Munich at the end of September.
Tevez is to return to the Etihad Stadium on Tuesday and resume his career with City that has been placed on hold for the last three and a half months.
Talking about the circumstances surrounding his refusal to warm up on September 27, the Argentina international said in a Fox Sports interview broadcast in translation on Sky Sports News: "I was kind of in a bad mood and when he brings on (Nigel) de Jong and takes off (Edin) Dzeko and we're losing 2-0 I thought it was a defensive substitution so I decided to sit back on the bench.
"I had already warmed up for 10 minutes and he has this attitude that he wants to lose 2-0 instead of 4-0.
"So I sat down and at the same time Dzeko comes off and is really angry and has a go at Mancini. He then sees the tunnel is closed so he has to sit down next to him and they start to have an argument.
"Dzeko was speaking Bosnian and Mancini would swear at him in Italian so it was a real mess.
"So I go and sit down and he doesn't see me because he's having this discussion. But then he turns around and sees me and you can imagine what happens.
"He's in the middle of an argument so then he tells me to keep on warming up and treats me like a dog.
"So when he spoke to me in that tone of voice, and I said 'No, I'm not going out'. So I was willing to play, but the coach was in such a foul mood because he had that argument with Dzeko.
"He started on me as well, started swearing at me, that was him, because I was very calm. I was just sitting on the bench and you can see from the footage that I was calm and just talking with (Pablo) Zabaleta. Mancini said some horrible things to me."
It appeared at one stage last month Tevez, who returned to Argentina after the row with City, would be shipped out as Inter Milan, AC Milan and Paris St Germain all showed an interest, but no move was forthcoming as he stayed at Eastlands.
Mancini made it clear on Sunday, following a 1-0 win at Aston Villa that enabled his side to return to the top of the Barclays Premier League, he was still seeking an apology from Tevez.
The player did adopt a conciliatory approach towards the City fans and claimed their angry reaction was understandable as they did not have the full facts.
"I believe they were misinformed, they weren't told the facts," he said in the interview shown and translated on Sky Sports News.
"So that when they were told I didn't want to play they naturally turned against me.
"If a player doesn't want to play for the team that's paying his wages it's only natural for them to turn against that player.
"And I couldn't understand what was going on. I swore like any player would. I gave everything to that club and when I saw them burning my shirt with my name on it or hurling insults at me it really hurt.
"I gave everything to that club and what I love above all is to play football."
Tevez's return to Manchester comes following negotiations between City's acting chief executive John MacBeath and Tevez's representative Kia Joorabchian.
Speaking on Sky Sports News, Joorabchian claimed Tevez's thoughts about the incident in Munich gave a misleading impression of his current frame of mind and claimed the player was determined once again to prove himself an asset for City, if given the chance.
To aid the situation, it is believed Tevez will drop his appeal to the Premier League against a six-week club fine, totalling around £1.2million.
Joorabchian said: "He's saying he will get himself ready as the club have requested him to do, because the club have said Carlos coming back can only be an asset to them.
"I've spoken to the club today, I've spoken to the club regularly on a daily basis and I think everyone agrees that from a football point of view Carlos can only be an asset.
"Now him and Mancini have obviously managed to resolve issues. What he had explained in his interview is how he felt back then. I think that the club and Carlos are taking this in a very positive way.
"He has a lot of repairs to do with the fans and he realises that and he has said that he's ready to apologise if he's done something wrong.
"And he's said that he sincerely never felt that he was doing something wrong at the time, and he understands that his actions may not have implied that."
Asked if Tevez will apologise to Mancini, Joorabchian said: "This is between Mancini and Carlos. I think one of the things that is important is that Mancini and Carlos resolve their issue, and I think they have pretty much resolved their issue, behind closed doors and I think what is important is that the football takes over."
As far as Tevez's team-mates are concerned, they will be glad to see him again in their push for the title over the final 13 matches.
"He is a good player and we'd welcome him back," said winger James Milner when asked by Press Association Sport as to his thoughts on the prospect of Tevez's return.
"He showed how good he was last year (scoring 24 goals). He was fantastic for us.
"What's gone on or what's happening is nothing really to do with the players, but if it gets sorted out, then great.
"It means it's another top player for us to add to the ranks."
Tevez claimed he would be ready to challenge for a place in the City side in two weeks.
"In two weeks I play, I think," he said in the same interview.
The striker revealed he was ready to apologise if the club deemed it necessary.
"I do not think I was wrong, but if they (the club) think so I apologise. I am ready to return, to win and do the best for the club's shirt," he added.
"Hopefully I can help City to be champions again. The most important thing for me is to return to get fit."I always said that at 28 I would retire. Today I say, 'No, I have much more to give'."