The Ivory Coast international said he had told match referee Ovidiu Hategan about the chants during the game in the Russian capital.
"It is quite disappointing," Toure said. "It is unbelievable and really, really sad to hear songs like that."
The midfielder called for tougher action by UEFA to tackle racism, which has been a longstanding problem in the game despite regular campaigns by European football's ruling body.
"I think UEFA need to do something strong. It would be nice if we could stop that... Every time we say something it continues, something has to be done to stop it," Toure said.
"I think UEFA has to be stronger, and hold all the clubs and all the fans that do that (responsible). Maybe they have a stadium ban. For me as an African player it is always sad to hear something like that and we need to do something about it."
Russa's state news agency RIA Novosti quoted Toure as suggesting a stadium ban for CSKA in European competition "for a couple of years or maybe a couple of months" — long enough that "the club will decide: 'OK, we have to educate the fans."
He also raised the prospect of teams boycotting the 2018 World Cup in Russia if the issue of racism wasn't dealt with.
RIA Novosti quoted Toure as saying: "If we aren't confident at the World Cup, coming to Russia, we don't come," and that he had also experienced racism when playing in the Ukrainian league. The Ivorian played for Metalurg Donetsk from 2003-05.
City manager Manuel Pellegrini echoed the call for action over the chants, saying "it was a pity and I hope we have the right measures."