Toure, pushed further forward after Mancini hooked Carlos Tevez, rewarded the manager's thinking with a late double.
Mancini said: "Yaya is an important player for us because he has experience. He won with Barca, he won trophies and he brought to us this experience for this reason.
"Yaya is a fantastic player, but I don't think you can win here because Yaya played well. We won here against Newcastle because all the team played really well and we deserved to win."