The 29-year-old, who has 68 caps for his country, was not included for their crucial World Cup qualifiers next month despite the fact they are struggling in their quest to reach Russia next summer.
The snub appears to have affected his club form with Allegri suggesting he looked out of sorts in the Champions League drubbing against Barcelona in midweek.
Therefore, he is looking for Higuian to step up to the plate for Juve and improve on the early-season form which has resulted in two goals from three Serie A outings.
Speaking ahead of the game against Sassuolo on Sunday, Allegri said: "He needs to be calm and play the way he knows how.
"Not being called up by Argentina is a strong incentive for him to repeat last season's performances and to improve, like all of us.
"He played a very good first half at Camp Nou and I am expecting a great game from him [on Sunday]."