The Serie A side were 2-0 down after 40 minutes on Wednesday courtesy of a Lionel Messi penalty and a Sergio Busquets effort. A Gerard Pique own goal reduced the arrears on the stroke of half-time before a second for Messi wrapped up a comfortable win for Gerardo Martino's men.
One of the talking points before the UEFA Champions League fixture was Allegri's decision to bench Italy international Balotelli, with Robinho chosen in a more advanced role.
Balotelli missed the first encounter between the two sides at San Siro with a thigh injury, and was unable to make a difference when he came off the bench on Wednesday.
And Allegri defended the decision not to name the 23-year-old in his starting XI, insisting the former Manchester City and Inter forward must learn to cope with the rigours of playing regular first-team football.
"It's simple I did it for Milan and Balotelli," Allegri said. "Mario had that injury on international duty and his performances were not sharp, so I preferred to start with the pairing that played in the first leg.
"He did some good things in the second half. Of course, people expect a lot from him, he has to improve and get accustomed to playing every three days, which he has never really done before coming to Milan, he was a reserve at Inter and Manchester City.
"It's tough both physically and psychologically. He did very well on a few occasions, while in others he delayed the pass a bit too long."
The loss leaves Milan second in Group H with five points from four games, with crucial fixtures against Celtic and Ajax still to come.
Milan have failed to win in their last five fixtures in all competitions, and Allegri will be looking for a response when the side travel to Chievo on Sunday.
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