The Bosnian showed his disgust during the Bayern Munich defeat at being subbed for a second consecutive game.
Afterwards Mancini said Dzeko could start games on the bench from now on if he wanted. But the player has since made a public apology and is set to start today at Blackburn.
Mancini said: "We don't have a problem. I am not disappointed in him because I can understand. Also sometimes I can make a mistake, I can apologise to the players.
"When you work every day, you can have some problems but it is important to resolve them very quickly."