Portuguese star Danny scored the only goal of the game after 35 minutes, however, Malaga's positive record against Milan meant that the Rossoneri would finish second in Group C regardless of the outcomes of the matchday six fixtures.
And it means Milan has still to win at home in the Europe's premier competition this term but Allegri is adamant that record should have ended on Tuesday.
"We created a lot of chances and played with a good pace but unfortunately we conceded in what was their only chance in the game," Allegri was quoted as saying on Milan's official website. "At the moment, the objective is Torino [in Serie A on Sunday], third place is still far away. We’ll be thinking of each game as it comes, in the Italian cup as well.
"Acerbi and Zapata played well and conceded very little to Zenit. We weren’t lacking in commitment, the team played well from a technical point of view even though the motivation can’t have been at its highest.
"We didn’t deserve to lose though, I’m disappointed for the players but we have to start not conceding goals. Twenty goals in 21 games is too much, we have to do better in certain situations.
"I’m happy with all the individual performances including Mesbah and Ambrosini, who both came back from injuries. We’ll see about Montolivo in the next few days, if there’s any risk, he won’t be on the pitch against Torino."