Reigning champions Barcelona were the team all the others were hoping to avoid, and ultimately it was Milan - along with BATE Borisov and Viktoria Plzen - who drew the short straw in Group H.
Nonetheless, Allegri is adamant his side will not be overwhelmed by the prospect of playing a side regarded by most as the best in the world at the moment, but conceded Milan will have their work cut out for them.
"We drew the strongest team [in Barcelona], but in our group we have two other teams within our reach," Allegri said following the draw in Monaco.
"I think the next round is fully within our grasp."
Allegri refused to rule out claiming a victory over Barcelona, but conceded Milan would have to be at their best if they were to have any chance of doing so.
"With Barcelona, it is a fascinating challenge.
"I believe that we must prepare ourselves to be able to play better.
"I think the game itself gives great stimulation and motivation. We are definitely in the best condition to deal with it."
Milan will travel to Barcelona in the opening matchday on September 13, before the return leg takes place in Italy on November 23.
Champions League Group Stage
|Group A||Group B||Group C||Group D|
|Bayern Munich||Trabzonspor||Manchester United||Olympique Lyonnais|
|Manchester City||LOSC Lille||FC Basle||Dinamo Zagreb|
|SSC Napoli||CSKA Moscow||Otelul Galati||Real Madrid|
|Group E||Group F||Group G||Group H|
|Valencia||Arsenal||Zenit St. petersburg||BATE Borisov|
|Bayer Leverkusen||Olympique Marseille||Shakhtar Donetsk||AC Milan|
|Racing Genk||Borussia Dortmund||APOEL||Viktoria Plzen|