14. ... Ne2
And Black wins. Not sure how you both missed that!
Evens Gambit
True with the fork 14 ...Ne2 but
After 14. ...Nc2
15. Bh5+ ...Kmove
16. Qf7#
Black Q can interpose at f6 to put off mate for one move.

Here's some analysis I did. I don't play the Italian game, and I didn't use a computer, so some of my lines may be wrong, but this is my take on things. You both clearly missed your mating threat, but you spotted it first, and that obviously decided things.
Does anyone have any comments on my knight sac idea for black?
EDIT: I just realized 14. Qd1 or 14. Qd3 is probably the correct move for white in the mainline. Anything else loses more material. But even after 14. Qd1 (Qd3) Kxf7 15. Qxd4, things look bad for white.
A nice game i played with the evens gambit, criticism is welcome