The 19-year-old was the goalscoring hero in his side's victory over Cagliari on Wednesday, and gave his coach a vote of confidence following its recent poor form
The young forward, who made his Italy debut against England in August, expressed his delight at the Rossoneri securing their first home win of the campaign, and believes the result can inspire the team to climb the table and revive their Scudetto bid.
Speaking to reporters after his double in Milan's 2-0 victory over Cagliari, El Shaarawy said: "Allegri is putting a lot of trust in me, he is making me play a lot this season.
"I'm young, but I try to give my all in every game and I think that I did well today. We had the right spirit today on the pitch, we started looking for a goal from the beginning."
Allegri was forced to watch the match from the stands after he received a one-match touchline ban for comments made towards the referee in the loss against Udinese.
However, El Shaarawy was in little doubt that the trainer has the confidence of the entire squad, as he dedicated the victory to the embattled 45-year-old.
"The victory is for Allegri and the fans," he continued. "We are with him, he has our trust.
"I'm happy because of today's victory. It will give us a lot of morale for the next games."
Milan currently sits in 10th place, having won only two of its five opening matches. The team's next test is away at Parma on Saturday.