The Rossoneri, who captured the Serie A title last season for the first time since 2004, are two points adrift of Juventus going into the game at Cagliari's Sant' Elia stadium.
"My team is a bit tired," Allegri said.
"But we have to make a last effort and take three points."
If Milan win, they could go top of the standings by midweek because Udinese, who have a perfect record at their Friuli stadium, host Juve on Wednesday night.
Udinese are level on 31 points with Milan.
"We hope that on Wednesday at Udine an interesting result happens," Allegri said.
"But the important thing is that we win."
While Milan won 2-0 against Siena on Saturday to continue an unbeaten run at home that began in December of 2010, Cagliari fell 2-0 at Chievo to drop to 12th place.
The Sardinians, who are coached by Davide Ballardini, have mustered just one win in their last 10 games.
"Cagliari are not going through the best of times," Allegri said.
"But they are a proud side and will want to bounce back.
"We will need aggressiveness, patience and be ready for their counter-attacks."
Allegri has confirmed that Alexandre Pato will partner Zlatan Ibrahimovic in attack.
The Brazilian forward came on as a substitute against Siena.
"Pato is improving and that's normal after the injury," Allegri said.
"He is slowly finding his best form."
Milan will welcome back goalkeeper Christian Abbiati as well as defender Gianluca Zambrotta from injury.
The hosts will be bolstered by the return of attacking midfielder Andrea Cossu from suspension.
However, they will be without midfielders Davide Biondini and Albin Ekdal, with the former serving a one-match ban and the latter out injured.