Toure was quoted in French football monthly magazine So Foot claiming he feels he is being victimised for participating in the ANC two years ago.
According to Mancini, Toure said he did not make the comments and the Italian on Tuesday said he accepts that and will not delve deeper.
Mancini, speaking at a press conference to preview Wednesday's Champions League clash with Bayern Munich, said: "I spoke about this with Kolo yesterday. He told me he didn't say anything about this.
"Kolo and I do not have any problem. He explained this to me and for me it is finished. It is okay now."
When asked if he believed Toure, Mancini said: "Yes I did, I believe him.
"I did not read the article so I don't know what Kolo said, I can say only yesterday at training he told me about this interview.
"I don't know what he said or didn't say."
Toure, who joined City in a ?16million deal from Arsenal in 2009 and captained the club prior to last season, has fallen down the pecking order at the Etihad Stadium.
The 30-year-old missed the start of the current campaign as he completed a six-month suspension for testing positive for a banned substance and has since found Vincent Kompany and Joleon Lescott difficult to dislodge.
However, this controversy comes after he started the club's last two matches, against Arsenal in the League Cup last week and in Saturday's Premier League defeat of Norwich.
Toure was quoted by So Foot as saying: "It's going to get more and more difficult for us, the Africans. To compete in the ANC, it's catastrophic these days.
"Coaches no longer want to sign players because of it. I am convinced that, if I am not playing, it's not only for football reasons."
Toure's lack of first-team action -- he has appeared just eight times this season -- has led to speculation he could leave the club in the January transfer window.
Paris Saint-Germain have been linked with the defender -- who is again likely to be involved in African Nations Cup action next month -- but Mancini insists he has no intention of letting him go.
Mancini added: "In this moment, no. Kolo is part of our plans for this year.
"Kolo is a good player, a good guy and if he plays or not -- because we have a lot of good players -- he is part of our plans.
"Kolo is important for us because he is experienced. In the summer he told me he wants to leave because he wants to play.
"I have respect for him and we can talk about this, but not now."
Source: AFP
Source: AFP