The Academy revealed the news on Twitter early Wednesday, but they later cleared the tweets and the pages detailing the performances on their official website.
The movie marked Cooper's directorial debut, and he had previously earned directing nominations for the film at the Golden Globes and the Critics' Choice Awards.
He recalled: "I was embarrassed".
Bradley Cooper was left feeling out when he was snubbed for a best director Oscar nomination. Her song Shallow has been nominated for Record of the Year, Song of the Year, Best Pop Duo/Group Performance, and Best Song Written for Visual Media.More news: Unai Emery reveals Arsenal loanee Denis Suarez trained alone on Monday
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Despite Cooper's disappointment, he realized that the lack of a nomination shouldn't be a factor in determining "whether I did my job or not".
Following the release of the film, the songstress has thanked her co-star Bradley for changing her life.
The drama has also been nominated for eight Oscars awards, including Best Picture, Best Actor, Best Actress, Best Supporting Actor, Sound Mixing, Adapted Screenplay, Original Song and Cinematography.
"She said, 'Don't try to sing it, '" he shared during his conversation with Oprah. When you talk, you're telling a story. "I was like, I just got to work harder to get one".
As the R&B singer-songwriter took her rightful place at the piano, the 40-year-old opened their duet crooning, "Tell me something, Keys, I hear you're set to host this year's Grammys".