The Rossoneri play the first leg at San Siro on February 20 and visit the Nou Camp on March 12 in the Second Round tie.
"We ended up with the strongest team in the world," Allegri told Milan Channel.
"We'll still try to get through this round, hoping to be luckier than we were last year."
These sides already clashed last season in both the group stage (drawing 2-2 at the Nou Camp and losing 3-2 at home) and the Quarter-Finals, where they drew 0-0 at San Siro and Milan lost 3-1 in Spain.
"This must be the fifth or sixth time we've been paired with Barcelona in a draw," sighed Milan director Umberto Gandini.
"Their visit has become almost a regular occurrence. We are growing and there is still time to improve, so we'll give our best and see what the result is.
"We're facing a side we know very well and they've had a few more problems than usual in the group stage this season. We hope that Milan can end this taboo and beat Barcelona.
"This is the biggest obstacle we could've drawn and it'll be a test of the side's maturity. We can win the Champions League, as Milan have already won it seven times."