Tevez angered manager Roberto Mancini when he appeared to refuse to leave the substitutes' bench and take the field during the second-half with City trailing 2-0.
Mancini later claimed the Argentinian would never play for him at City again before saying he would consult the club's owner about the way forward.
But Tevez claimed he did not refuse to play and also said he was ready to fulfil his obligations to the club.
Tevez said in his statement "I would like to apologise to all Manchester City fans, with whom I have always had a strong relationship, for any misunderstanding that occurred in Munich.
"They understand that when I am on the pitch I have always given my best for the club.
"In Munich on Tuesday I had warmed up and was ready to play. This is not the right time to get into specific details as to why this did not happen. But I wish to state that I never refused to play.
"There was some confusion on the bench and I believe my position may have been misunderstood.
"Going forward I am ready to play when required and to fulfil my obligations."
Mancini said he would speak with Manchester City chairman Khaldoon al-Mubarak in the next few days to decide what to do.
Mancini intended to introduce Tevez as a substitute for the final half an hour.
However, in a move that seems certain to trigger his eventual departure from the club, the 27-year-old appeared to simply say: "No."
"In the next days, we will speak with Khaldoon," said Mancini.
"It is normal. He is the chairman. He decides everything.
"If I decided, yes (he would leave). He wanted to leave last year. I helped him for two years every time. He refused to play.
"I cannot accept this behaviour from him.
"I decide the substitutions, not Carlos."
Tevez did not look particularly perturbed by the situation he has landed himself in when he left the stadium.
However, the Blues did get extra security at the airport to ensure angry fans did not encroach beyond acceptable levels.
Having agitated for a move for so long, Tevez will surely get his wish, and there was no apology for his actions immediately after the game.
"I have been professional during all my time here," he told Sky Sports News.
"Last season I was the top scorer and I wanted to leave for family reasons but I keep trying to do my best."
Nevertheless, it is difficult to see how Mancini could want him in his dressing room after making such unforgiving comments.
"Do you think at Bayern Munich one player can play like this? Or Milan or Manchester United? No," he said.
"There were 30 minutes to the end. There was time to change the game.
"Carlos didn't play at the start of the season because he didn't do a pre-season for three years. He is not ready to play."
This would have been bad enough, in addition to being condemned to defeat by two goals in eight first-half minutes from Mario Gomez.
But Mancini also had to contend with a strop from Edin Dzeko, who took exception to being replaced by Nigel de Jong 10 minutes into the second half as City tried to stop themselves being submerged in their opponents' bombardment.
"I should be unhappy with this performance, not Edin," said Mancini.
"But he played a poor game. If you play every three days, it is impossible that one player can always play well and that he can always stay on the pitch for 90 minutes."
But there was also a stern warning for the giant Bosnian.
"This is the last time one player leaves the pitch and moves his head like this," Mancini continued.
"I can understand a player is disappointed. I can understand inside he can be upset if he thinks he has played well. But I am the manager. I decide everything."