Milan are eleventh in Serie A with just seven points from their opening six games.
They face city rivals Inter Milan on Sunday, and Abbiati has said that the players are behind the boss.
"I have never had any problems with Allegri," he told Gazzetta dello Sport. "But I can assure you, since he arrived the players have always been behind him.
"Being Milan's coach isn't easy but he is handling it well. His age allows him to have a great connection with the players.
"During the matches he's the one who is in charge, but off the pitch he talks and makes jokes."
Allegri has come in for criticism from some fans and sections of the media recently and Abbiati has urged the supporters to get behind the team in such a crucial game.
He added: "I want to see a stadium full of passionate people when we face Inter tomorrow."
Inter are in third place in Serie A, four points off leaders Juventus.