The Rossoneri's 3-1 victory at Anderlecht means that they cannot be caught by either Wednesday night's opponents or Zenit St Petersburg, and will go through as runners up behind Group C winners Malaga.
Stephan El Shaarawy and a stunning Philippe Mexes bicycle kick put the Serie A side in control at the Constant Vanden Stock Stadium, and although the hosts were reduced to 10 men after Bram Nuytinck saw red, Tom de Sutter's strike 12 minutes before time brought the Belgian side back into the contest.
Substitute Alex Pato netted in added time to seal the win and their progression, however Allegri knows his team were far from perfect.
"We did well even if at the end we suffered a bit, something that shouldn't happen," he told the club's official website.
"This is a step that the team has to take, improving in possession of the ball.
"I'm happy for the team and the club which has achieved the first target of the season with a game in hand. It was important not to get to the last match with it all to play for against Zenit.
"We need more experience which we'll get as we're young."
And Allegri praised two of his goalscorers and was surprised to see Mexes' effort end up in the back of the net.
"When Mexes took that shot, I thought it went wide but he scored," the boss added.
"He was criticised harshly after Fiorentina and in the last two games he has played very well. Pato took a knock but it shouldn't be anything serious.
"This was a good game for him to come off the bench and he showed that. In the changing rooms, I simply said that maybe I hadn't explained myself."