Uefa has charged CSKA with racist behaviour of its fans after the their defeat to City, and the Russian club will face a disciplinary hearing on 30 October.
Touré has spoken of his disgust at hearing monkey chants and RIA Novosti quoted the Ivory Coast midfielder as saying: "If we aren't confident at the World Cup, coming to Russia, we don't come."
The Ivory Coast international claimed he was racially abused "a few times" by "groups" of supporters, rather than a handful of individuals and added he was "furious".
Asked whether Russia needs to treat racism more seriously before they host the World Cup, Touré said: "Of course they do. It's very important. Otherwise if we are not confident coming to the World Cup in Russia, we don't come."
Both Fifa and Uefa have declined to comment.
CSKA Moscow are expected to challenge the UEFA charge after issuing a statement saying they were "surprised and disappointed" by Touré and City officials' allegations.
A club statement said: "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 Džeko. Why the Ivorian midfielder took it as all being directed at him is not clear."
CSKA also quoted their own Ivory Coast player, striker Seydou Doumbia, as saying he did not hear any racist abuse.
Doumbia said: "I didn't hear anything like that from the CSKA fans.
"Yes, they're always noisy in supporting the team and try to put as much pressure as possible on our opponents, but they wouldn't ever allow themselves to come out with racist chants. So my Ivory Coast colleague is clearly exaggerating."
CSKA said they had never been sanctioned for racist abuse in all their years in European competition and will "continue to fight against racism".
The match referee Ovidiu Hategan from Romania, meanwhile, has been criticised for failing to follow UEFA's procedures and issue a stadium announcement warning that the chants must cease.