Coach Fabio Melillo's side came from 2-0 down to level the game at Coverciano after 90 minutes - and then had a number of good chances to win the game in extra-time.
But a decisive goal would not come and, after a rollercoaster penalty shootout, it was the Nerazzurri who would eventually come out victorious in the end.
"The girls did brilliantly," Melillo said after the game. "Their comeback was impressive.
"In extra-time we played with desire, we really fought hard. I hope the fans understand and appreciate women's football a bit more.
"We deserved to win, it would have been a fair way to cap off an extraordinary season. We've helped develop players that will have a chance with the first-team too."
See photos from the game in the gallery below.
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