Television pictures showed the supporters shouting, hurling insults and throwing objects at the team bus as it pulled out of the stadium.
Some of the chanting was aimed at the club's flamboyant president Maurizio Zamparini.
Some fireworks were thrown at riot police but the Ansa news agency said that the situation was under control.
Zamparini has fired three coaches this season, and reinstated one of them less than a month later.
He dispensed with Giuseppe Sannino after only three games, saying the coach's relationship with the team had deteriorated, and replaced him with Gian Piero Gasperini.
Gasperini was fired after his team lost to Atalanta at the start of February and replaced by Alberto Malesani, who was himself sacked after only three games in charge. Zamparini then re-hired Gasperini.
Sunday's defeat left Palermo bottom of the table with 21 points.
Club director Giorgio Perinetti denied suggestions that Gasperini might quit after Sunday's defeat, which came only two matches into his second stint.
"Gasperini's a fighter and I don't think he will want to quit," he told RAI television. "We want to finish the championship in a dignified manner and we must fight until the end."
Palermo, who won the Italian Cup two seasons ago, have not won in their last 14 Serie A games.