How should have I defended this?

I had some trouble with this opening...I still managed to win but I need to see what I did wrong.

The idea for that opening is to get you to play 5... Nxd5 so white can sacrifice the knight like he did.  Typically the black king will take the knight (as you did)then move to e6 to protect his knight so he can be up in material.  White's goal is to lure the king out to the middle of the board and attack attack attack.  I've seen your way of playing the opening a lot too...that is, moving the king back to e8 after taking the white knight and accepting the loss of the f pawn and the ability to castle.  Here's what I've learned is the way to defend.

It can go a few ways from there.  I'm sure other people have other ways of dealing with it too.  I hope that helps.

 Both sides played very well.

In case of 1. e5 e4, the rapid move of the black bishop to Bb4 aims at attacking f7 square rapidly together with Qf3, Qh5, Ng5.
The black move Nf6 prevents the black queen from attacking by Qf3, Qh5.
But, it can't stop the black knight's attack Ng5.
In order to stop the Ng5 attack, the black can move its h-file pawn to h6 in advance (though it weakens the king side castle).