The 25-year-old was disqualified from the competition this week after producers discovered that he had been charged with two crimes in 2011 and had used false names with police.
However, Jones has now told People that he informed producers of his past when he applied for the show.
"They did have a question [in which you had to admit] that you were arrested, and that I did do," he said. "And they did an extensive background check. When I went home [after my first elimination] and then I went back, I thought, 'They've done the research at this point'. I was a little bit confused."
Jones continued: "I did not know I was breaking the rules, because before I went, I had to obtain a lawyer and take care of some fines before I could go. I just thought everything was taken care of."
However, Jones said that he is doing "very, very well" following his elimination from American Idol and explained that he is optimistic about his future.
"People will judge me or hold it against me, but I don't know anyone that doesn't have a past," he said. "Everyone has a past. It's not like I shot someone or assaulted anyone. I was younger. I got caught driving with a suspended license. I gave a false name. I'm not trying to say it was okay, but I'll be alright."
American Idol continues on Wednesday at 8/7c on Fox.
> American Idol result: Top 11 singer eliminated
> American Idol Top 11 results show: Live blog
Watch Jermaine Jones performing on American Idol below: