The two sides drew 1-1 in Holland last week leaving the tie finely balanced for the return clash at the San Siro.
Milan suffered a shock 2-1 defeat to Hellas Verona in their Serie A opener at the weekend but Allegri is eager to put that behind him and is hopeful that his side can replicate the standards of their performance in Eindhoven.
"There should be a proactive attitude," he told a press conference.
"We know the importance of the game. We face a team that plays good football and that has created difficulties.
"In the first leg we gave a good performance and we have to think about winning this game and not conceding goals.
"They are a team that creates a lot and we can not think of doing a defensive game. We must start from the good performance in Eindhoven."
The two teams have won eight European Cups between them, with Milan contributing seven of those, and skipper Riccardo Montolivo understand the importance of Europe's premier club competition.
"We realize the importance of the game," he said. We have a responsibility and we feel it.
"We have to play for our pride, because we want to play the Champions League."
Celtic boss Neil Lennon has accused Shakhter Karagandy boss Viktor Kumykov of boastful disrespect ahead of their second-leg tie at Parkhead.
The Hoops are 2-0 down from the game against the Kazakh champions in Astana and Shakhter's Russian coach has been quoted as saying they would "score a pair of goals" in Glasgow to take them through to the group stages.
At Celtic's training complex in Lennoxtown, Hoops manager Lennon hit back, saying: "We know we have to win the game by three goals.
"If they score we need to score four, if they score two - according to their manager - then we need to score five.
"I think it (their confidence) is very dangerous and it can always come back to bite you.
"This is a two-game tie and it is disrespectful to my team as well.
"I don't need to motivate my players for tomorrow night but if they want to keep talking the way they are doing then that's fine."
Zenit St Petersburg take a 4-1 lead into their clash with Pacos de Ferreira but manager Luciano Spaletti is refusing to be complacent despite his side seemingly having one foot in the group stages.
"Some people think it will be an easy match after 4-1," he said. "The people who say that won't be the ones on the pitch. The ones who go out to play are the ones who know what to do and who don't consider our opponent a pushover.
"Because you can't joke around with matches of this level. Every match is very important to us and this one even more.
"We want to participate in the Champions League. We want Zenit's name to be in the list of participants."
In the night's other games, Viktoria Plzen travel to NK Maribor with a 3-1 lead while Real Sociedad will look to defend a 2-0 lead at home against Lyon.