It has been a disappointing start to the season for Il Diavolo who currently sit 13th in Serie A on 14 points from 12 games.
However, the 76-year-old believes Allegri is still the right man for the coaching role, insisting that changing the boss during the campaign is not his club's style.
“If Allegri is here, then, it is because I have faith in him,” he told reporters. “This is an unfortunate period, but let us not forget what he has won.
“Milan have a tradition. In 26 years, we’ve changed the coach during the course of a season on only two occasions. We are serious people, we have a good relationship with the tactician.”
However, he admitted that letting go of Ballon d'Or nominee Zlatan Ibrahimovic and others in the summer was not easy, but a financially necessary decision.
“There is regret over Ibra, but you have to do the maths," he continued.
“We saved €130m [£104m] with their sales and nobody, during this economic climate, would have turned that down.
“You see real fans in times of difficulty. I expect the team to be supported. After 26 years of caviar and champagne, patience is needed.”
The club president concluded by commenting on current Milan players.
“El Shaarawy is a solid kid with his feet on the ground. If only he'd change his hairstyle ...
“Alexandre Pato is a great champion. He was the most untouchable player we had, then, he had this series of injuries. He needs to pick himself up, but he has a desire to get back to his levels.
“As for Riccardo Montolivo, he is a playmaker, he reminds me of Pirlo."