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.
"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."
