"I've gotten tons of awards and I believe when it's my time to get a Grammy, I'll get a Grammy," she said with a laugh.
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The 30-year-old had one of last year's biggest hits with the multiplatinum dance-pop anthem "Starships." Her sophomore album, "Pink Friday: Roman Reloaded," has reached gold status and launched other hits on the rap and R&B charts.
But Minaj, who received three Grammy nominations last year, including best new artist and best rap album for her platinum debut, "Pink Friday," was shut out when this year's nominations were announced.
"I think that the Grammys had a different reason, that I do not want to discuss ... and that's just between me and them," she said in a recent interview. "But I respect their organization and I'll get a Grammy eventually. I'm not worried about it."
A representative for The Recording Academy didn't immediately respond to an email Tuesday seeking comment.
Minaj was featured on Ludacris' "My Chick Bad," which was nominated for a 2011 Grammy Award, before she released her first album.
She was criticized when she released her sophomore album last April for taking on a pop-and-electronic sound that echoed Katy Perry, Rihanna and Ke$ha. "Roman Reloaded" is a mesh of hip-hop, dance, pop, R&B and reggae flavors, and producers included radio hit makers like RedOne and Dr. Luke.
"I understand that artists and critics make a big deal over the Grammys. But when I go to my shows and I'm selling out arenas in London, and when I'm in Australia and Japan, there aren't any Grammys there," she said. "There are human beings who I've touched. There are human beings who are inspired by me, who I love dearly. And that's what my career is based on."
Minaj, who is a new judge on "American Idol" alongside Mariah Carey and Keith Urban, said she would probably be upset if she doesn't earn Grammy respect later in her career.
"You do feel good when you get awards and accolades. Maybe if I had been doing this for 10 years and I thought like, 'Oh my god, I've put out 10 albums' -- maybe it would have hurt my feelings. But I still feel so new that it's like, 'Charge it to the game,'" she said. "It's part of the game."
The Grammys will air live on CBS from the Staples Center in Los Angeles on Feb. 10.