Kwadwo Asamoah scored the only goal of the game three minutes before the break as Juventus dominated possession in the opening period.
The visitors showed a slight improvement after the break, but were unable to find a way back into the match.
"When you play against Juventus, a lot depends on them," Montella is quoted as telling Sky Sport Italia. "We were very deep in the first half, but despite that Juve didn’t really have that many scoring opportunities.
"It wasn't the game we wanted to play and we were more advanced in the second half with a few chances to equalise. It's a shame.
"Everyone knows Juve are a very strong side in every aspect, so in all honesty I thought Fiorentina played a very good second half and could've equalised.
"The team slowly gained confidence and was under less intense pressure. I am satisfied with the reaction after an unusual first half for us, as we rarely play with that attitude, but we need faith and optimism."
The teams meet again in the UEFA Europa League last 16 on Thursday, with the second leg taking place on March 20, and Montella is certain his charges will be better prepared.
"We know what awaits us on Thursday and have the chance to have our say using our characteristics," he added.
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