Manchester City may be the world's richest club, thanks to the hundreds of millions invested in three years by Sheikh Mansour of Abu Dhabi, but Tevez's antics were more like those of a Sunday morning park player than a top professional earning more than 200,000 pounds per week.
Mancini, who also had angry words with their Bosnia striker Edin Dzeko after substituting him, told reporters that as far as he was concerned Tevez was "finished" at City.
The Italian, looking visibly shocked, told a news conference: "I am really disappointed because it is Carlos.
"This can't happen in a top club -- to refuse to go in to help his team mates. What I said to Carlos is between me, him and the team.
"But if we want to improve as a team Carlos can't play with us. With me, he is finished."
Bayern were deserved winners at the Allianz Arena, where Mario Gomez scored two first-half goals, to extend their winning sequence to 10 matches in all competitions.
They lead the group with six points, followed by Napoli, who beat Villarreal 2-0, on four points. City are third with one point while the Spaniards are without a point.
While City were floundering in Munich, their neighbours were also having problems of their own at home against Basel despite taking a 2-0 lead in the opening 17 minutes with a brace from young striker Danny Welbeck.
Their defence was shaky all night and Old Trafford was stunned as Fabian Frei and Alexander Frei struck in quick succession midway through the second half to make it 2-2.
The latter then converted a penalty after United got in a tangle in their own area with Antonio Valencia bundling over Marco Strellar.
United were heading for only their second defeat in 33 home matches in the competition when Young headed home in the 90th minute to salvage a point.Ferguson plans squad rotation for United
"We were careless and there was a lack of concentration throughout the side at times," United manager Alex Ferguson said. "We let them create a lot of chances but we rescued it.
"I told them to finish it off at halftime and it is a wake-up call for us. If you are lax then with the quality in the Champions League you will suffer."
Inter Milan, the 2009-10 champions, earned their first points in Group B as new coach Claudio Ranieri's dream start to the job continued.
Mauro Zarate scored the late winner to give Ranieri his second victory since taking over from sacked Gian Piero Gasperini, the other victory coming in last weekend's league game against Bologna.
"I think we beat a very good team tonight," Ranieri, whose side had led 2-0 at one stage, told a news conference. "We played well, passed the ball well and also controlled the tempo," added the former AS Roma, Juventus and Chelsea manager.
Inter are in second spot with three points, one behind Turkish club Trabzonspor who drew 1-1 at home to Lille.
Inter's former manager Jose Mourinho enjoyed a straightforward evening in Madrid as nine-times European Cup winners Real cruised past Ajax to take control of Group D.
Ronaldo gave them the lead in the 25th minute at the Bernabeu before Kaka and Karim Benzema struck either side of halftime.
Real lead the group by two points from Olympique Lyon who have four thanks to their 2-0 win at home to Dinamo Zagreb.