The San Siro outfit are looking to finish the group stages with a win and sustain their unbeaten home record in the current European campaign and, although they have already qualified for the knockout stages, Allegri is determined not to let that affect the result on Tuesday.
"We must win," he told Gazzetta.it
"In matches where we had already qualified, AC Milan almost never did well. It is going to be a game in order to extend the streak of results. Winning is good.
"Winning helps us to stay calm and we must also prepare for the championship race. It is not a race you need to qualify, but if you do not get a positive result it is only two or three days to reconsider and we do not have that time."
Zenit are looking for a result that betters that of the side bottom of the group, Anderlecht, to gain a place in the Europa League.
The fixture is scheduled for Tuesday December 4, 2012 19:45 UTC at San Siro.