I'm confused(computer analysis)

I just finished a computer analysis of a game I played earlier today. Here is the beginning of the game up to the move I'm confused about:

My last move, Bc5, was annotated as "Bc5?!" by the computer analysis engine. I'm not claiming that was my best move. What I'm confused about is the computer claims Nxe4 would have been the best move, which, apparently, would have been followed by white's Qe2. Is the computer confused or am I missing something here? Nxe4 obviously kills my Knight.

Should I not have as much faith in this chess engine as I do, or is there something deeper I'm not seeing?

actually if you wil go for Nxe4 than you will get Rook

...Nxe4

fxe4  Qh4+

g3 Qxe4+

Ne2 Qxh1

It gave the question mark because you would have gotten a free pawn if you played Nxe4.  That or you would end up roughly a rook up like the line in my diagram.

It gave the exclamation sign because it was still a valid idea. 

Holy crap.

if you opponent move king than I think codition will be worse..

lol

(The only thing I don't agree with is giving a "?!" to Bc5.  That's a good move too...but Nxe4 was more incisive there.)

It's not that easy.

After 1.e4 e5 2.c4 Nf6 3.f3 Nxe4 4.fxe4 Qh4+ 5.Ke2 Qxe4+ 6.Kf2 Bc5+ 7.d4 Bxd4+ 8.Kg3 h5 9.h3 the typical Damiano trick 9...Bxb2 does not work here as after 10.Bd3 Black cannot play 10...Qa4.

I guess Black has some advantage after 9...Qg6+, but I'd rather play 3...Bc5! which clamps nicely to the weakened g1-a7 diagonal, and white's position is simply a mess.

like everyone said, if you find your opponent playing the Damiano's Defence, you take his e-pawn with your knight

Wow, quite instructive. Look at this little gem that is just in the forum posts. Thanks, everyone. This is the most interesting thing I have read, watched, or heard about in days. I appreciate high rated players taking time out to crack open these lines of play.

yes thank you everyone

By the way, it's nice to see a fellow IPU follower.