On the road at Juventus Stadium in the continental competition, the Florence-based club arrested an early deficit to take the slight advantage into the second leg when Mario Gomez equalised with 11 minutes to play.
"A coach prepares a strategy ahead of a game, but some work and others don't. Against Juve you have to prepare several, as they have so many options and movements," Montella told Sky Sport Italia.
"Initially we decided to push up and keep the ball wide to avoid them going through the middle and slowly we got the measure of them. I like this style of football, attacking and taking some risks.
"I don't know how many games (Juan) Cuadrado has played, but he can be on the bench occasionally.
"I made a tactical choice too, as we needed players who would dialogue with a certain logic and his strength is more of an illogical approach."
Cuadrado and Manuel Pasqual did not appear against Juve on Thursday, with Montella opting to try and control possession against the Italian champions.
"We need to keep the ball, otherwise we struggle," he said.
"Against Juve that is even more necessary, as they are a stronger team and physically tougher, so we have to play between the lines.
"There were positive signs despite the difficult start, as they were forcing our full-backs to stay tight. I liked the first half perhaps more than the second, as Fiorentina were always in it and almost all Juve's scoring opportunities were on set plays.
"We always tried to take the initiative and I saw my team enjoy its football in possession."
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