The Brit, who is a judge on the show and an executive producer on American Idol, hit out at contestants Misha Belfer and Mitchel Kibel after they performed a same-sex samba routine.
On the show's season premiere on Thursday, Lythgoe told the pair, "I think you probably alienate a lot of our audience. I mean, we've always had the guys dance together on the show, but they've never really done it in each other's arms before.
"Do you know what? I'd like to see you both dancing with a girl."
After the show, Lythgoe also backed up his comments on the panel by taking to his Twitter page, writing: "The same-sex ballroom guys did remind me of Blades of Glory. However, I'm not a fan of Brokeback ballroom."
Officials at gay-rights group Gay & Lesbian Alliance Against Defamation (GLAAD) immediately demanded an apology from the TV titan, calling his remarks "unacceptable" and an act of "blatant homophobia."
Lythgoe admitted his regrets in a comment issued on Saturday: "I sincerely regret the fact that I have upset people with the poor word choices and comments I made both during the taping of the So You Think You Can Dance audition and on my personal status update (on Twitter.com). I am not homophobic and it was extremely upsetting for me to be classed as such.
"I have been forthright and consistent with my opinion, as a judge, that professional male dancers should move with strength and agility -- like Gene Kelly and Rudolph Nureyev. I now realize how this could be misconstrued. I have been a dancer, and involved in the dance world, for nearly 50 years. Professionally and personally, I believe the sexual orientation of an auditioner or contestant is irrelevant. All that said, the fact that I have unintentionally upset people is distressing to me and it is obvious I have made mistakes that I must learn from. I trust that my humor will be more sensitive and mindful moving forward."
And GLAAD bosses have accepted the producer's words of remorse: "We certainly appreciate the dialogue, and the opportunity for Nigel to help further educate people about how words and images matter. His sincere words are appreciated, and we look forward to words, images and representations of the LGBT community on So You Think You Can Dance that will be fair, accurate and inclusive in the future."
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