He has asked the youngster to continue scoring in the biggest games, as Mario Balotelli misses the match through injury.
"El Shaarawy has to continue playing the way he has been recently," Allegri told a Press conference.
"He is a great player, but one season of good performances is not enough to leave a mark on the history of this club.
"I also ask for the support of the fans tomorrow. We feel their presence on the field - they have to be our twelfth man.
"Saturday's match is an excellent opportunity to overtake Lazio in the standings. It is certainly an important game in terms of third place.
"We have to win."