Defeat to Fiorentina last weekend has left Milan languishing in 13th position in Serie A, just five points above the relegation zone and eight adrift of the top five and a place in Europe next season.
On Wednesday, they travel to face Anderlecht in the Champions League needing to avoid defeat to keep alive their hopes of reaching the knockout stage of the competition.
First, though, they travel to Serie A high-flyers Napoli needing to put things right on the domestic front, and Allegri is confident he can turn things around in the coming weeks.
"There is still time to lift ourselves up," he said. "Between now and December 22, there are still plenty of important matches in the league and the Champions League and we are concentrating on them.
"Despite our ugly league position, we are the side with statistically the most possession, so we just need to defend better and be more alert in certain situations."
That may be one reason why Berlusconi paid the team a visit today, to keep them on their toes ahead of a crucial few weeks.
Allegri did not see his visit as a vote of confidence in his own position, though, saying he "enjoys a great personal relationship" with the president, who "has always shown his faith in me."
"He was in great form and I hope we are on the same level tomorrow [Saturday]," added Allegri.