"The PFA's opinion, based on all the evidence presented, is that Carlos Tevez never refused to play for the club," a statement said.
Following a disciplinary hearing that took place on Friday where PFA chief Gordon Taylor was in attendance, the Argentine international was fined on Tuesday after it was deemed he had committed five separate breaches of contract.
They included "an obligation to participate in any matches in which the player is selected to play... when directed by a club official."
The PFA disagreed with Tuesday's ruling and have given their support to Tevez.
"This is accepted by the club in that the charge against Carlos made at the hearing was not one of refusing to play," the statement added.
"As such the PFA considers that there is no justification for a fine other than up to the prescribed sanction of two weeks' wages agreed by the FA, the Premier League and PFA.
"The PFA has informed the Manchester City Football Club accordingly and Carlos will continue to be supported by the PFA in this regard."
After the 2-0 defeat at Bayern, furious manager Roberto Mancini told reporters Tevez had refused his request to go on as a second-half substitute.
The player later denied the accusation, saying he had not been asked to go on but to warm up and he felt he had already warmed up sufficiently.
Mancini said the player would never play for him again and media reports have speculated that Tevez, who again asked for a move in the last transfer window as he is unhappy in Manchester, will be sold in January whatever happens with the case.
