The 2-0 win won the Coppa Italia semi-final 3-2 on aggregate.
"It was a very difficult game and before celebrating Fiorentina's performance, I must compliment Udinese for their efforts over both legs. They caused us a lot of problems," Viola coach Vincenzo Montella told Rai Sport.
"Having said that, over 180 minutes I feel it was a deserved win and we will enjoy it with our fans, patrons and the whole city. We hope it can become a big moment for Florence.
"We are growing a great deal, although there are some physical problems when playing so often. We saw great team spirit tonight and I'd say the desire was what allowed us to win even more than our technique."
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