The Viola lost 2-1 at the Stadio Olimpico, but Montella felt that his team produced a good display despite the result.
"We had several chances to take the lead. Roma had a few opportunities and took the most of them, whereas we didn't," he told Sky Sport Italia.
"It was a fascinating game with two teams playing great football. I think either side could've won considering the performances, but we have to accept the defeat, even though three points would've been important."
Fiorentina are currently fifth in the Serie A table.