"Nicki is very deferential to Mariah," Lythgoe told reporters at the So You Think You Can Dance finale on Tuesday. "[Nicki] says, 'You do realize you're auditioning in front of this incredible singer here, why would you want to choose her song to sing?' "
Veteran judge Randy Jackson, who is sitting alongside Carey, Minaj and country star Keith Urban for Idol's 12th season, which premieres in January, may feel a little unappreciated, according to Lythgoe.
"The kids that come in are either super fans of Nicki ... or they are fans of Mariah and they've been to Camp Mariah. And then Keith Urban [also has his] fans. So, Randy is sort of left," he said.
Lythgoe – who called the first day of auditions in New York City "the best first day I've ever had" – joked that the judges are almost too helpful to the hopeful contestants.
"It really has already become very constructive," he said of the lengthy critiques, "to the point that I'm saying, 'For Christ's sake, shut up. Let's move on.' "
Reporting by PATRICK GOMEZ