Toure described as "unbelievable and very very sad" the monkey chants reportedly directed at him by fans of the Russian capital club during Wednesday's Champions League game won by City 2-1.
"We want to stop that and UEFA have to be strong, maybe close the stadium," Toure told Britain's Sky television at the end of the match.
City manager Manuel Pellegrini added: "It is a pity that these things happen and I hope that the right measures (are taken)."
The 2011-12 English Premier League champions have made an official complaint to UEFA over the alleged chanting, which prompted calls for a tougher line to be taken on bigotry.
UEFA confirmed that it would look into the racist chanting claims, as well the throwing of smoke bombs, at its disciplinary commission on October 30.
European football has been hit by a string of high-profile incidents against black players, most notably AC Milan's Kevin-Prince Boateng, who walked off the pitch during a friendly earlier this year because of racist chanting.
UEFA is this week mounting a "No to Racism" week with the Football Against Racism (FARE) in Europe group, which has seen anti-racism and discrimination messages broadcast during Champions League and Europa League matches.
Toure was wearing a "No to Racism" armband in Moscow.
UEFA has vowed tougher sanctions against clubs found guilty of racism, including playing matches behind closed doors and shutting problem areas of grounds.
But the chairman of British football anti-racism group Kick It Out, Herman Ouseley, said more needed to be done.
"(The referee) failed to do his duty last night and that is a clear issue that UEFA should be dealing with," he told BBC radio.
"UEFA and (world football governing body) FIFA take us for mugs. That can't go on any longer."
Everton manager Roberto Martinez agreed, saying it was "time to make a strong stand".
In Moscow, however, the accusations levelled at one of the 2018 World Cup hosts' top clubs drew a mixed response, with the club itself claiming that Toure had been mistaken.
"Having carefully studied the video of the game, we found no racist insults from fans of CSKA," a club statement read.
"In many occasions, especially during attacks on our goal, fans booed and whistled to put pressure on rival players, but regardless of their race."
The Moscow club's Ivorian forward Seydou Doumbia claimed in an interview on the front page of Russia's popular Sport Express daily that his compatriot had "clearly overreacted."
"I've never heard any such thing from our fans," Doumbia said.
"Sure, they loudly support our team and try to put as much pressure on the opponents as possible. But no one permits themselves racist chanting."
Russia's UEFA spokesman Sergei Borisov told the ITAR-TASS news agency that he was at the match and "heard no racist chanting".
But state television's vesti.ru website conceded that "CSKA Moscow could face serious problems" if City's complaint was upheld.
The accusations are particularly sensitive to Russia after they won the right to host the 2018 World Cup following a bitter battle against front-runners led by England.
Russia's Moskovsky Komsomolets tabloid was especially cynical about the amount of attention devoted to the issue in the British media.
"This situation played right into the hands of the British media, which once again started playing the old record about how the 2018 World Cup was awarded to a country where racism flourishes," said the paper.
"The British media has long been waging a campaign to boycott major football tournaments played in Eastern European countries."
But Russia's 2018 World Cup organising committee acknowledged that football in Russia did have a racism issue.
"What is clear is that football is uniquely positioned to educate fans in combating this global issue," it said.
"The 2018 World Cup in Russia, in particular, can act as a catalyst to positively change the mindsets and behaviour across all involved in Russian football over the next four years."
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