After victory over Siena in the last eight, Fiorentina now face a two-legged semi-final against Udinese - with the first game to take place at Stadio Friuli on Tuesday.
With the competition winners earning a place in next season's UEFA Europa League, Montella is keen for his players to maintain their focus but knows Francesco Guidolin's side will provide a stern test.
"We're really determined to make the final," he said on Monday. "Getting there and having already guaranteed a Europa League spot for next season in February would be a fantastic achievement.
"Udinese are a good, strong, young team. They adapt well to their opponents, they are not defensive and they will be a dangerous opponent for us.
"They're a team with many qualities that defend and counter in a very organised way. They know how to soak up pressure. It's a game with a high-risk factor for us."
Fiorentina have not lifted the trophy since 2001, while their opponents have never won the competition in their 118-year history.
‘The pure simplicity of the way Slot has managed the squad is probably the biggest thing I could say about him. It’s not broken, so let’s get on with it’: Liverpool legend full of admiration for Jurgen Klopp's successor at Anfield
‘I trained at Spurs and thought they’d give me a chance. But I received a letter thanking me but saying they didn’t think I was good enough – I was gutted’: How Tottenham missed out on signing Wales legend John Toshack
