The Ivory Coast midfielder claimed that he was the subject of abusive chanting from some sections of the crowd during the 2-1 UEFA Champions League victory at the Arena Khimki on Wednesday, telling the media after the match that he had reported the taunts to referee Ovidiu Hategan.
He also used the opportunity to call on the European governing body to take action, adding: "It's unbelievable. I think UEFA needs to do something strong."
City have now followed that with an official complaint of their own, with a club statement on Thursday adding: "Manchester City FC can confirm that it has today issued a written formal complaint to UEFA regarding the events of last night's game against CSKA Moscow.
"It follows the complaint which was raised to the UEFA delegate immediately after the conclusion of the game.
"It is noted that UEFA have opened proceedings into the matter and we await the findings in due course."
The incident has once again brought the issue of racism in European football into sharp focus, with Toure's City team-mate Vincent Kompany leading the calls for a firm stance to be taken in order to rid the game of the problem.
He tweeted: "Racist chants again in Moscow. We've all said enough. @UEFAcom, @GovernmentRF, CSKA, all eyes are on you now. #StopRacism", while Everton manager Roberto Martinez added: "It is a real shame.
"I don't think we should be talking about these issues any more. It is important that FIFA and all the football authorities can do something about it.
"They must not let it go and accept it. It must not be another moment that can just be brushed aside."
UEFA confirmed to Perform on Thursday that they will wait for the referee's report before launching an investigation, but CSKA have been quick to refute allegations of racism.
They insist that their fans did not single out Toure for abuse.
A statement on the club's official website read: "We are surprised and disappointed by statements made by Manchester City player Yaya Toure alleging racially motivated insults from fans of CSKA.
"Having carefully studied the video of the game, we found no racist insults from fans of CSKA. In many occasions, especially during attacks on our goal, fans booed and whistled to put pressure on rival players, but regardless of their race.
"In particular, this happened with Alvaro Negredo and Edin Dzeko. Why the Ivorian midfielder took it as all being directed at him is not clear.
"It is an important fact that during the entire history of European competition our club has never observed, or been punished for, acts of racism from fans.
"In any case, we deplore this incident, although we believe accusations of racism are unfounded."
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