Milan finished third in Serie A last season, but have not dominated at home and in Europe like they once did.
"We are the first Italian club in Europe, just look at the UEFA rankings," Galliani told reporters at the player's unveiling.
"I don't like this story that is told to us. We won the Scudetto [Serie A] three years ago. We were first up until April two years ago and last year we finished third.
"I claim both the past and present of Milan with pride. Ricky [Kaka], I say these things because you have not arrived at a team of bums."
Milan's next game is against Torino on September 15.