Lythgoe's 'hard feelings' over Idol
The British TV producer has been ditched from the US singing competition after several years, in what was apparently part of a shake-up in a bid to boost falling ratings.
He told Access Hollywood: "Of course I've got hard feelings. I'm p****d off."
However, Nigel said he understood that the decision wasn't personal.
He said: "But, in truth, you say at the end of the day that this has been a fantastic journey and it really has [been] for me, personally. And I don't have hard feelings in that sense. This wasn't a personal, you know, 'You're fired! We hate you.' This was, 'Look, we really want to make this programme work and we believe we need to do something different'."
It will be Nigel's second exit from the show. After starting on Idol in 2002 he left in 2008, then returned in 2010.
News he had been axed followed the announcement that judges Nicki Minaj, Mariah Carey and Randy Jackson were all leaving the show. It is not known whether the fourth judge, country singer Keith Urban, will be back.
Nigel, who will still be working with Fox on dance show So You Think You Can Dance, thinks Idol needs to re-focus its efforts on appealing to the whole family.
"I believe the issue is that we lost our way, that we went for a young audience when really, we're a family show," he said.
"When we came over here, I said, 'We are going for targeting this middle age group that will bring the kids in and the grandparents.' And families I think, nowadays, feel very guilty they aren't together enough so if you have a programme that attracts an entire family, you get what you want, which is that younger age group anyway."