The 26-year-old's car was kicked by several fans as he left Roma's Trigoria training complex on Tuesday.
Fans shouted at him to leave the club.
Barusso has spent four years at Roma but has made only three league appearances.
As he is from a non-EU country he is occupying one of the limited spaces in the squad allowed for other players.
As fans kicked his car, they shouted: "You must go."
"People took out their frustrations with Roma's failure to bring in players. It was a terrible incident."
Barusso, who has spent the vast majority of his time at Roma out on loan, with Galatasaray in Turkey and then Italian sides Siena, Brescia, Torino and Livorno, has refused all transfer propositions this summer.
"Ahmed is calm and until he is presented with a really interesting offer, either from Italy or from abroad, he won't consider leaving," added Giusti.
Due to the complicated Serie A rules regarding non-EU players, Roma would need to release Barusso in order to bring in another non-EU player.