The Italian side were drawn in Group C with Russian side Zenit St Petersburg, Belgian outfit Anderlecht and the financially-stricken Spaniards Malaga, and Allegri has claimed Milan are more than capable of winning the group.
"Surely a group like this is winnable," said Allegri.
"Compared to the last two seasons, there is one very strong team, but three teams where all things are equal. Our goal is first place to give us a better draw in the second round."
Milan begin their Champions League campaign at home to Anderlecht on September 18.