"Champions League games are never easy. We knew Zenit's result, so winning tonight was very important to secure qualification," Allegri told Mediaset.
"We have achieved our first target of the season and the lads fully deserved it. We suffered at times and got the final ball wrong at times, but only really risked on the counter-attack and on set plays.
"We should've done better in defence after they went down to 10 men, as they were throwing crosses in there and hoping for the best.
"We had started well, then I think we were too hasty and tried too many long balls rather than making the right decisions in attack. We knew there was space behind their four defenders, but failed to find it in the first half."