Montella admits Fiorentina are 'annoying' referees
Montella's men received two red cards and conceded a penalty but still managed to come from behind twice to earn a point at the Stadio Ennio Tardini.
Modibo Diakite and Borja Valero were sent off for Fiorentina, while Parma substitute Gianni Munari also saw red.
Montella said his club, who sit fourth in the Serie A, were perhaps annoying officials.
"It is true that our behaviour must improve. It is also true that I am not tense about the situation," he told a news conference.
"The club and I are relaxed about refereeing, we do not fire up the players in that sense, even if they may well be tense.
"Our players must learn they cannot try to get vigilante justice, even if they think that decisions have gone unfairly against them. If we are patient, then we can improve.
"We will take a step back but the other side also has to take a step forward and come towards us, because I get the feeling we are becoming annoying and that's a paradox.
"The players are becoming annoying to those who referee games and maybe I and the club are too."
Antonio Cassano and Juan Cuadrado traded goals before half-time but Parma regained the lead thanks to an Amauri penalty on 51 minutes.
Diakite was sent off after picking up his second yellow card but Fiorentina still managed an equaliser, as substitute Matias Fernandez curled in a 25-yard free-kick.
Munari and Valero saw red in stoppage time after a scuffle in a wall at a set-piece.
Montella appeared to be shouting at referee Andrea Gervasoni post-game but said he was trying to shake hands with the official.
"I thought people were obliged to shake hands after the final whistle but apparently that is not the case," he said.
"Referees can salute you from a distance or later in the tunnel, which he explained to me afterwards.
"I expected Gervasoni in midfield but he didn't come my way...maybe he didn't want to get insulted."