The Brazilian playmaker set up his compatriot Robinho for the opening goal, and Allegri was quick to highlight the overall display from the former Real Madrid man.
"Kaka had an extraordinary game and he proved he is a champion," Allegri told Sky Sport Italia.
"I don't mean just in technical terms, as we all know that, but he worked so hard and even acted as a full-back at times when harassing the Barcelona players.
"Kaka proved once again to be a champion it's not enough to have great feet, but to work hard and put the effort in."
The 31-year-old re-joined Milan in the summer transfer window.