The Rossoneri endured a nightmare start to their campaign, which led to calls for Allegri's head from some sections of the Milan faithful.
However, Ambrosini said that Allegri has done a good job at the San Siro and believes that the team have turned a corner.
"It has been a difficult time for everyone," Ambrosini told Milan Channel. "But the coach has done a very good job.
"He has been questioned by everyone from outside, but he has remained humble and had the courage to change things around.
"It is good management by the owners. We have always had faith, and the fans have understood."
Milan are 10th in Serie A.