The Viola claimed a 2-1 win in their quarter-final tie and will now face Udinese in the last four.
"Is the Cup a primary objective? Just as all the games are," Montella told reporters. "And we try in every game we are delighted to have now reached the semi-final, overcoming a tough and difficult opponent who made us sweat more than expected.
"Now we will play another important game against another very difficult opponent (Udinese).
"Is it better to meet Udinese than Milan? When you arrive in the semi-finals, you are there on merit and if Udinese have eliminated Inter and Milan, clearly they can create difficulty for us."
Fiorentina have won seven of their past eight matches in all competitions and currently sit fourth in the Serie A table.