Tevez scored and provided a constant threat at City beat Chelsea by three goals to two at Villa Park on Sunday.
Mancini has said that Tevez is ready to perform to his maximum because he has the hunger to play football again.
He told Sky Sports News: "I am very happy because Carlos this year has worked very well in pre-season, and his form is better than last year.
"Also this year he wants to play football. For a player, it is difficult when he does not play. Last season he did not play for six months and this is difficult.
"I expect him to be a very important player. He is a top player if he wants to play."
City begin the defence of their Premier League title against newly-promoted Southampton on Sunday, August 19.