Pato recently returned to Milan’s first team following an injury lay-off and scored his first goal of the season in a 1-1 Champions League draw at home to Malaga.
But his penalty miss in a 3-1 defeat to Fiorentina at the San Siro on Sunday was seen by some fans as a costly mistake.
According to Corriere dello Sport newspaper a group of angry Milan fans waiting for Pato to leave the stadium surrounded and banged on his car and launched verbal threats at the Brazilian.
Pato, who is in a relationship with Barbara Berlusconi, the daughter of current AC Milan owner Silvio Berlusconi, earned the penalty on the half hour as Fiorentina led 1-0 but sent his effort from the spot over the crossbar.
La Viola went on to take a 2-0 lead and after Pato was substituted at halftime in favour of Giampaolo Pazzini the Italian reduced arrears only for Mounir El Hamdauoi to score a superb third goal for the visitors.
Victory could have propelled Milan up the Serie A table but instead the Rossoneri were left in 13th place, 17 points behind leaders Juventus.
Milan’s worst start to the season comes two years after coach Massimiliano Allegri steered them to the title in his first year in charge and a runner-up place behind Juve last season.
Allegri said after the game: “I’m very disappointed because we had a chance to jump up the table into sixth place and start to put things in order. I don’t know how it would have ended had Pato scored the penalty.”