The mercurial forward remains a source of recurring frustration for Mancini but the City boss still wants to coax the best out of him.
Mancini was highly critical of the 21-year-old's overall display in Saturday's clash with Sunderland despite his two goals in the 3-3 draw at the Etihad Stadium.
Since then there have also been unconfirmed reports of a dressing-room argument with team-mate Yaya Toure and speculation City would be willing to consider offers for him in the summer.
But when asked if he was prepared to give up on the former Inter Milan youngster, Mancini said: "No.
"I am frustrated because sometimes I think it is not possible that a player with his class and his technique can play a game like this.
"I think he is young and I hope for him he can improve very quickly for his future.
"A player like Mario in the Premier League should score one or two goals every game."
Last week was another eventful one in the colourful career of Balotelli.
It began with an unexpected appearance at an Inter Milan press conference, which was followed by a training-ground spat with Mancini.
Mancini then said he could not trust the player, whose afternoon against Sunderland was also noted for a row with Aleksandar Kolarov over who should take a free-kick.
"This was a bad moment," Mancini said.
"I think a professional player can't do what they did in that moment, when we were losing 3-1."
Although City recovered from that deficit to claim a draw, the two dropped points could ultimately prove costly in the Barclays Premier League title race.
Yet Mancini insists he will not be giving up the fight.
He said: "We should be strong, I believe always.
"The message is always the same - we will do everything to win this title."
When asked what he said to the players after Saturday's game, Mancini said: "Nothing because they were so tired.
"I said only, 'believe in yourselves' because we have seven games - 21 points. I think with 92 points we will win the title."