Balotelli attitude must improve, says Allegri
Balotelli was sent off for dissent after the final whistle of his team's 2-1 loss to Napoli on Sunday, when he had a penalty saved and also scored a late goal.
Allegri praised the 23-year-old for his performance, but said he should know better than to argue with officials after the game.
"I didn't speak to Mario, but I'm told he received another booking. He received a fair few kicks, including many from behind, though he overall had a good game," Allegri told Sky Sport Italia.
"When games are over it's better to stay quiet and I am against hysteria.
"It's best to just shut up and leave rather than stay there arguing with the referee, as it's not going to change anything. Balotelli needs to improve that."
Miguel Angel Britos' sixth-minute header and Gonzalo Higuain's second-half strike set up the visitors' victory.
Balotelli had a penalty saved by Pepe Reina on the hour-mark before he curled in delightful strike from just outside the area in the first minute of stoppage time.
Allegri said it was Milan's best performance of the league season, apart from the first 10 minutes of the clash.
"Tonight the team put in a decent performance in technical terms, though we were naive in the first 10 minutes and conceded that avoidable goal," he said.
"It was in a way our best performance of the Serie A season so far. We were lucky to get back the 2-2 draw at Torino, so we paid for that good fortune this time around.
"If we were going to play badly and earn a result, I preferred to play well and lose, even if this was a head-to-head.
"We could've done better in the box, but apart from the opening 10 minutes it was our best performance of the season."
Milan are 11th after picking up just four points from as many league games, but Allegri said he had solutions in mind for their slow start to the season.
"We must try to pick up as many points as possible now. Napoli are one of the candidates for the Scudetto and we played on a par with them overall despite missing many key players," Allegri said.
"I already have ideas on how to fix things, but I need some of the players to recover from injuries first."