Two goals down from the first leg of their last-16 meeting with Dynamo Kiev, City were left to play for almost an hour with 10 men after Balotelli was sent off for planting his studs into Goran Popov's chest and thigh.
Although the Blues did pull one back through Aleksandar Kolarov before the break, a second goal that would have forced the encounter into extra-time eluded them, leaving Mancini a frustrated man at the final whistle.
"If it stays 11 versus 11, we would have probably scored two or three goals," he claimed.
"I didn't see the foul properly but I am very disappointed because in a game like this it is very difficult if you pick up a red card, and you can pick up a red card for doing something stupid.
"The problem for Mario is that he thinks he could be a fantastic player. But when he does something stupid like that, it is difficult for me, difficult for him and difficult for the team."