The Professional Footballers' Association (PFA) released a statement on Thursday in support of Tevez, who had been fined four weeks wages by City following a disciplinary hearing last week.
The club said they were disappointed the PFA had refused to ratify their sanction and were concerned by an apparent conflict of interest between PFA chief executive Gordon Taylor and the disciplinary process.
"Manchester City Football Club has received notification from the Players' Union that it will not support a four-week fine as a penalty for the actions of misconduct of Carlos Tevez," the club said in a statement on their website.
"Manchester City is disappointed by the apparent PFA conflict of interest evident in this process.
"Carlos Tevez has been personally represented throughout by the PFA chief executive, on whose considerations the club has been informed that the PFA has made its decision.
"Manchester City has been in constant dialogue with the PFA since September 28th. Today's PFA decision is a departure from the Club's understanding of that dialogue.
"Without recourse to the PFA decision available, the maximum two-week fine provided for in standard player contracts will now be applied in relation to the misconduct of Carlos Tevez."
Earlier in the day, the PFA had questioned City's decision to fine Tevez more than two weeks' wages.
The Argentine was fined on Tuesday after it was deemed he had committed five separate breaches of contract.
"The PFA's opinion, based on all the evidence presented, is that Carlos Tevez never refused to play for the club," a statement said.
"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."
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 Tevez 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.
