Mancini claims Tevez refused to come off the bench in Germany on Tuesday and is adamant the Argentina forward will never play for City again.
Tevez denies the allegation and insists he misunderstood what Mancini was saying.
But the former Manchester United star, who has been keen to leave Eastlands for several months, is currently suspended while the club's hierarchy carry out interviews with Mancini, his coaching staff and the players who were with Tevez on the bench.
It is thought that Tevez's team-mate Pablo Zabaleta was supportive of the Argentine and shouted back at Mancini, who also argued with Edin Dzeko after substituting the Bosnian during the Bayern defeat.
However, England defender Richards has become the first City player to criticise Tevez for his actions.
"Carlos's reaction in Munich was wrong. It was something he shouldn't have done," Richards told The People.
"There was always going to be a bit of tension because Carlos is a top player and hasn't been getting in the team. But there was no sign that he was going to do what he did.
"I like Carlos. He's probably still the best player that I have played with and I'll always be grateful he came to City and helped us achieve what we did last season.
"He's been our best player for the last couple of years and won't be happy the manager has been picking other strikers ahead of him.
"But we are a top team now. We can't just be about one or two players because if you want to challenge for the big trophies it has to be about the strength of your squad."
Tevez has mostly been used as a substitute by Mancini since his failed attempt to enginner a transfer during the close-season and it has been reported that the striker is angry he hasn't played more often.
Richards, who had to fight his way into Mancini's plans last season, admits Tevez should just knuckle down and focus on winning back his place rather than throwing a temper tantrum.
"There's a lesson for us to learn here. If we want to be a top team then as individuals we have to sacrifice ourselves," Richards said.
"I went through it myself. I might not be a big name like Carlos Tevez but I am an England international and I thought I should be playing in every game.
"You do get emotional. Your pride does hurt. I found it hard when I wasn't in the team and at times I did struggle to just keep my head down and say nothing.
"I thought Carlos was just waiting for his chance to show what he could do."
Meanwhile, Vincent Kompany -- who replaced Tevez as City captain at the start of this season -- also insists the saga has not affected the squad.
"No doubt people will be expecting Manchester City to fall apart after what happened in Munich, but that isn't going to happen," Kompany said.
"Okay, so some things have happened that aren't good, but people should just calm down a little bit.
"We will bounce back very quickly. I can't give any answer about Carlos Tevez because I don't know what was going through his mind and I don't know what happened because I was on the pitch."
Source: AFP
Source: AFP