He said that in the end of the 12th episode of the second season ("The Descent")!
He was sad and found a girl named Jessica so as to tell her his biggest and hidden secrets and thoughts! Then he wanted to bite her, he regretted and he left her but in the end he bit her.
It was such an emotional and sad scene :( I loved Damon even more when I saw it <3
"I'm not human. And I miss it. I miss it more than anything in the world. That is my secret"- Damon Salvatore
This was said in season 2, episode 12 towards the very end.