The Serie A side were already confirmed as Group K winners before Thursday's game, but Montella was still "ashamed" by the manner of the defeat.
Goals from Sergei Kontsevoi and Nemanja Nikolic put the visitors in control at Stadio Artemio Franchi before Marko Marin netted a late consolation for Fiorentina.
"I am not happy with the performance in terms of attitude and will," said Montella in La Gazzetta Dello Sport. "We showed less intensity and concentration than our opponents.
"I am ashamed to be losing like this, I'm sorry for the fans of Fiorentina and apologise to them."
Fiorentina had to take off winger Juan Cuadrado early on through injury, but 17-year-old substitute Simone Minelli did help to set up their late goal.
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