Viola boss Paulo Sousa was unhappy with some key incidents during the game.
“You know I try to avoid commenting on incidents, enough with this culture of suspicion, you can't be here doubting everything," Montella told Mediaset Premium.
“I have great admiration and respect for Sousa, but I'm afraid he has learned the culture of suspicion rather too well from us Italians. I don't want to get into this controversy, as the culture of suspicion is not for me.
“We lacked a little courage, initiative and confidence. I saw a game where, in the first half, Fiorentina were slightly superior. In the second we did better, but didn't make the most of the three or four chances we created.
“Fiorentina had more of the ball, but that was to a degree because we decided to allow them that. I don't know how we get more courageous if not with experience. When we tried to take the initiative today, we created chances and got to their box, so we need to continue doing more of that.
“We were too passive at the start and looked timid. The teams got stretched out as time wore on and I liked the desire my side showed. We faced a difficult exam and I think we passed it, albeit not with flying colours."