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Mariah Carey sang a furious tune on Sunday — with the pop diva’s camp blaming her disastrous New Year’s Eve performance on “sabotage” by the TV show’s producers.

Carey’s manager sent a letter on New Year’s Day to Dick Clark Productions, saying they set the “Emotions” singer up for failure by letting her take the stage before more than a million people in Times Square — and millions more watching at home — with malfunctioning sound gear.

“You know her inner ears were NOT working and your entire production team did not set her up to win,” the manager, Stella Bulochnikov, wrote to Mark Shimmel, whose company produced Carey’s TV nightmare, which was broadcast live on ABC.

“AND MARIAH KEPT TELLING THEM [something was wrong] ON STAGE IN REAL TIME,” Bulochnikov typed in all caps in the letter, a copy of which was obtained by The Post.

“THEY KEPT IGNORING HER. SHE TOOK A HIT HONORING HER COMMITMENT TO YOU. I SHOULD HAVE PULLED HER OFF THE STAGE THIS IS SABOTAGE.”

She ended the letter by demanding a “formal apology” and saying the singer may pursue legal action if no mea culpa is forthcoming.

Bulochnikov later told The Post she doesn’t believe Dick Clark producers deliberately caused the diva’s equipment to malfunction — causing her to be humiliated as she floundered on stage for several minutes, unable to sing her own hit songs. But Bulochnikov does think the company saw an opportunity once the performance started going south.

“Once things went wrong, they took the decision to keep rolling and make her look like a train wreck for the ratings,” said Bulochnikov. “They owe her a public apology.”

A source in Carey’s camp said she told the producers several times that her earpiece — through which the singer can hear her music and people talking to her — started malfunctioning during a pre-performance interview with Ryan Seacrest.

“They kept telling us, ‘Don’t worry, the earpiece will work when we go live. It will be on a different frequency,’” the source told The Post. “But the earpiece didn’t work. She couldn’t hear the music.”

In a moment of desperation, Carey took out her earpiece during the performance, with the hope of hearing the music from the speakers in Times Square.

“It was just too loud,” the source said. “All she could hear [was] the crowd.”

While Dick Clark Productions declined to respond, a source claimed the real sound issue was that “Mariah didn’t rehearse.”

A few hours after the show, Mariah took to Twitter to declare, “S–t happens. Have a happy and healthy new year everybody! Here’s to making more headlines in 2017.”

The drama came two years after Carey kept fans waiting for three hours in freezing rain before pre-taping a number for the 2014 Rockefeller Center Christmas tree lighting.

She ended up performing live at the lighting the next night, and later blasted that show’s producers for leaking audio of her failing to hit the high notes on her hit “All I Want for Christmas Is You.”