Tevez scored a stunning goal as City came from behind to win 3-2 against Roberto Di Matteo's side.
Mancini said: "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.
"Last year we had Carlos for the last 10 games and it was important because he scored five or six goals.
"But he was not 100%. This year is the first time in four or five years he has done a pre-season and, for every player, this is important."