The move back to Juve has left a sour taste for some Milan supporters, who targeted the veteran defender with jeers during the Nations League clash.
Mancini criticised the fans and said there should never be a repeat when players are representing their country at the international level.
"It was a mistake for fans to be booing Bonucci," he told a news conference following the scoreless draw.
"This is a type of protest that shouldn't happen when you're playing for the national team.
"Hopefully it only lasted for 15 minutes but I repeat it shouldn't happen because when Italy is playing, the crowd should support the players."
Bonucci too referenced the repeated jeering, saying that fans who booed him were "idiots" while insisting he is only worried about the opinions of his team-mates and coaches.
Italy will finish second in Group 3 of League A, with Portugal moving into the Nations League Finals following Saturday's draw.