The 19-year-old's team-mate Leonardo Bonucci sparked outrage after the game when he claimed Kean was partly to blame for celebrating in front of the home fans.
But Kean's international manager, Mancini, has stood by the forward and called for a clampdown on racism in the stands.
"The attitude used against Kean is unbearable," Mancini told reporters. "We must stigmatize the racists, we can't stand for it any longer.
"We need to take a stand, act even more harshly so that these things end."
On the teenager's celebrations, Mancini said: "He is a boy and maybe next time he probably won't do it, but maybe he felt in difficulty."
The former Inter and Manchester City boss took over the Azzurri after they failed to qualify for the 2018 World Cup, and as they attempt to secure a place in Euro 2020, Mancini is concerned by the lack of a gap between the club season and the tournament.
"If the next season ended a little before May 24, it would be better, that's for sure," he continued. "Now let's see what can be done."
Roma midfielder Nicolo Zaniolo could play in his first international tournament at the Euros next year after making his Italy debut last month at the age of 19.
The teenager has been linked with a number of top European clubs, but his father has insisted he will renew his Roma contract this summer, and Mancini has hinted that could be best for his development.
"I don't know if it's better to stay in Rome even without playing for trophies," the Italy boss said.
"He is a good player, a young guy who still needs to learn a lot and has to grow and improve. The most important thing for him is to play, and play regularly as he is doing now."