Allegri was named coach of Milan last week, over 11 years after his last spell in charge.
Asked about playing for Allegri, Abbiati told La Gazzetta dello Sport: "If he got angry in my day too? Sure. He said things in everyone's face, even to the big names, but then he didn't hold a grudge. When he spoke, he did it for the good of the team."
Quizzed about potential tension between Allegri and director Zlatan Ibrahimovic, Abbiati continued: "It is normal that there are comparisons between the players and the coaches.
"It happens when you have the same goal: to win. If there was a reason in the past, but the important thing is not to hold a grudge. I don't think there will be any problems with their coexistence with Milan."
Return to Milan?
And on returning to San Siro, Abbiati replied: "This year I never came ... The first thing Marco said to me (Landucci) was 'I'll wait for you at Milanello'.
"I will go there willingly because I respect Allegri's staff very much, made up of professionals and exceptional men.
"In particular, I am a friend of Landucci: do you think that when I played I had his gloves ... I hope to see Milan often win: what happened in the last season must be forgotten quickly and with Max I think it is possible to do it."