The coach praised the Italy international for earning the Rossoneri a draw at the Armando Picchi, but demanded more concentration while defending leads from the rest of the team
The enigmatic forward's level of commitment has been repeatedly questioned by the press this season, but he netted a fine double at the Armando Picchi, rescuing his side from defeat with a sensational free kick with just seven minutes to go, having earlier opened the scoring with a close-range finish.
But though Allegri was generous in his praise of Balotelli, who has now hit four goals in his last three games, the Livorno native criticised the rest of the team for failing to hold on to their seventh-minute lead.
"I think Mario is very serene at the moment; he played well in both halves. He still has margin for improvement but he can be devastating," the Rossoneri boss told reporters.
"It’s not easy for anyone to come here and play but once we took the lead we should have defended better as a team. Today I celebrated my 100th game in Serie A and I would have liked to celebrate it differently.
"We endured too much pressure from Livorno and the second goal could have been avoided. It’s disappointing because all football games have to be faced in the same way.
"Credit to Livorno, but it was our fault as well. Let’s hope that this match will serve as a lesson to understand that there are no easy matches."
The struggling San Siro outfit are currently languishing in eighth place in Serie A, 22 points behind leaders Juventus.