Toure reactivated his Twitter account on Monday following his side's 1-0 derby victory over Manchester United on Sunday and posted: "Great to be back on Twitter after a good win yesterday. Now my focus is on the next game...Happy Monday everyone!!"
Police were then alerted to reports of racial abuse against the Ivory Coast midfielder made on the social networking site.
The 31-year-old has now called for more to be done to tackle abuse.
"For me it's a disgrace to be honest," Toure told BBC Sport.
"We need to do something to try to tell people those kinds of behaviour have to stop. I want those people to understand what they're doing is wrong.
"To have such aggression in sport, I can't understand that. That's why I've been trying to fight it.
"Football doesn't have a colour. We're just people from all over the world trying to enjoy the game.
"I never see this in rugby, I never see that in tennis or anything else. I don't know where it's coming from."
City manager Manuel Pellegrini does not believe that Toure will be adversely affected by the situation.
"I think Yaya is an experienced player. He is always trying to fight against those things but I don't think he will have any problem about that, to play in the way he knows [how] to do it," he said ahead of Wednesday's UEFA Champions League clash with CSKA Moscow.
"I read the news about what happened, but I think the people in charge will do the right things."
