The opening moves that you played were NOT the Fried Liver attack. Fried Liver attack goes like this:
As I pointed out in the diagram, most of the time Ng5 is dubious, even if Bc4 threatening the f7-pawn is played. Why? Because usually the knight can be chased back, and white will lose tempo that way. It was also a dubious move in the game you played, I post the correct line for black here as a puzzle.
So, what should you learn from this game? You shouldn't play moves that break the opening principles unless you know very well what you are doing. And in this case, you didn't. You were lucky your opponent made a horrible blunder with 4. ...h6?? that gave the game away immediately. In the future I recommend focusing in the basic opening principles when playing the opening instead of trying to get into a highly theoretical opening line you don't know at all. All in all, I find that the beginners here on chess.com are way too enthusiastic about the Fried Liver attack, so much that it hurts their play and improvement.
And also, I recommend posting your losses, as you can learn a lot more from them.
EDIT:
AFTER (first solve it by yourself :]) solving the puzzle, click on the question mark that'd show the correct moves: that way you'll see my annotations about the position.
anyway, I don't think you should try to find the best way to meet Ng5: the situations are different, and there is no magic move that'd refute Ng5 every time.
So this was obviously a great game for me, opponent resigning after 13 moves but my idea was to try out the Fried Liver attack. Now I’ve always thought it can only be used when black uses the two knight defence but am I right in thinking that I could have still played it if instead of him -playing 4. …h6 he played 4…d5 where I would then take on d5, his knight recaptures and I bring my Queen out to f3 and the fun begins. As it happens it was a strange move on his behalf and I took advantage but it seems you only need one knight out for the Fried Liver to work (even though I didn't get round to it). Also, any tips where I could have done any better here. Pretty happy with my game.