The Argentina international is expected to be out for at least a fortnight which will see him miss the FA Cup semi-final against his old Manchester United at Wembley on Saturday.
He limped off in Monday's 3-0 defeat to Liverpool with a hamstring problem and was replaced by Balotelli, who himself ended up being taken off after another disappointing performance.
The Italian's form has been hit and miss to say the least since his arrival from Inter Milan last summer, due in part to injury and disciplinary problems on and off the field.
Mancini is desperate to get a more consistent level from the 20-year-old, who's attitude has also been called into question, but his manager is keeping his fingers crossed he can step up for the big occasion.
City are seeking to book a place in their first cup final since 1981 as they look to end a 35-year draught for silverware.
"Mario knows he must take more responsibility," said Mancini.
"We have six league games, plus the semi-final and the final. I hope Mario can score important goals.
"He could be the hero. On Saturday, if he plays, he has a chance to do well.
"Maybe if he scores a goal it could take us to the final. That would change his year."
The City boss hasn't totally given up hope on Tevez's being available for the game with United although in truth, it does seem like wishful thinking.
"It will be very difficult for Saturday but he should be okay to return in two weeks," added Mancini.