The Serie A leaders go into the encounter at the Renzo Barbera stadium on the back of last weekend's 1-1 draw against Juventus, a result that kept the Rossoneri at the top of the standings, just one point ahead of the Turin giants who have a game in hand.
Juventus host Chievo before playing a rearranged fixture at Bologna four days later.
"This is a crucial game in view of the Scudetto," Allegri said. "To remain at the top of the standings this weekend is important for us even though Juventus will have a chance to overtake us next week.
"Hence, we have to win."
However, Milan have not won at Palermo since the 2005-06 campaign while tomorrow's opponents have won 10 of their 12 games at home this season.
"With respect to last year, they have changed many players," Allegri said. "But their mentality when playing at home has not changed. They are difficult team to face and they have great players.
"We cannot afford to underestimate this game."
The Rossoneri will be bolstered by the return of leading scorer Zlatan Ibrahimovic, who missed the last three league games through suspension.
"I see Ibrahimovic being really motivated for this game," Allegri said. "I'm happy his punishment is finally over."
Palermo will be looking to make amends for last weekend's 4-1 defeat at Siena.
The Sicilians, winless on the road this season, lie eighth in the standings thanks to their solid form at home and coach Bortolo Mutti said: "We have always done well at home, but at the same time we know that on Saturday we will face a team that has great motivation and a very strong technical structure."
The hosts will be without suspended defender Federico Balzaretti.
Milan are without defender Philippe Mexes, who serves the first of a three-match ban, while strikers Maxi Lopez, Antonio Cassano and Alexandre Pato are all on the casualty list.