It emerged earlier this week that Peterson, who controversially beat Khan in December to capture the Bolton fighter's WBA and IBF titles, had tested positive for a banned steroid.
The news cast doubt over the pair's May 19 rematch in Las Vegas and Khan has confirmed that the bout has been scrapped.
He said: "First of all I'm disappointed because I trained very hard for this fight.
"It was only 10 days away from the fight where my dad came knocking on my bedroom door and said to me, 'look, Lamont Peterson's failed his drug test and the fight's no longer going to happen'.
"It was a big shock for me. My head was all over the place, I really, really wanted to win my titles back and have the fight. But the truth's come out now and it just proves that Lamont Peterson was a cheat really.
"It hurt me more than anything because I really did want to go in there and put on a performance and show the world how good Amir Khan is."
Asked about how he can get his belts back, Khan said: "I think whoever I fight next they'll put the titles on the line or we still go through the process and we might get the titles back and the fight that we had last time will be a no-contest."
Khan is now looking to get back in the ring this summer.
He said: "I'm looking at fighting June 30. I'm in great shape now."