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Barbra Streisand argued that sexism cost her Oscar nominations for “Yentl” and “The Prince of Tides” during a spirited public interview at the Tribeca Film Festival on Saturday. But it wasn’t just men who balked at the idea of a woman calling the shots on a major motion picture.

“There were a lot of older people,” Streisand told her interlocutor Robert Rodriguez. “They don’t want to see a woman director.”

“I don’t know how many women wanted to see a woman director,” she added.

Streisand said that jealousy and competitiveness are partly to blame for women turning on one of their own gender. As evidence, she claimed that female critics were harsher than their male counterparts to “Yentl.” Three decades after the drama’s release, a review by former New York Times critic Janet Maslin still seemed to rankle the recording star and filmmaker. She remained put out by Maslin’s reference to Streisand’s use of a “pillbox-contoured designer yarmulke” in the film.

“None of [the female critics] talked about what the movie was trying to say,” Streisand said. “It was not about what the movie was about — a celebration of women and all they could be.”

Oh, and for the record, Streisand said the yarmulke was authentic to the film’s early 20th century Polish setting.

“Yentl,” the story of a woman who dresses like a man so she can study Talmudic Law, was nominated for five Oscars, missing out on a Best Picture nod. “The Prince of Tides,” a drama about an emotionally damaged man who falls for his psychiatrist, got seven nominations, included film of the year. In both cases, Streisand’s name was left off the director’s short list. Eight years separated the two films.

Streisand said she was pleased that being overlooked focused attention on discrimination towards women, but she said the experience of being snubbed for “Yentl” had something to do with her long hiatus.

“I must have been more hurt than I thought, because I didn’t want to direct for years,” she said.

Rodriguez, a Mexican director best known for such blood-spattered actions films as “El Mariachi,” would seem an odd choice to moderate a panel with Streisand, a performer whose style is brassy and sentimental. But the Hispanic director said he was a massive fan of Streisand’s work, telling her that she gave him the courage to break into movies.

“You inspired me to go into an industry where I felt I didn’t have voice,” he said.

Rodriguez argued that Streisand had shattered a glass ceiling for other female filmmakers such as Kathryn Bigelow — a notion that Streisand discouraged.

“Not enough women are directing now,” said Streisand. “I love when I see a woman’s name on the film, and then I want to see it be good.”

Streisand said she originally wanted to just focus on acting and recording, but disagreements with Sydney Pollack on 1973’s “The Way We Were” pushed her in a different direction. She’d been horrified when scenes that she felt illustrated why her on-screen relationship with Robert Redford’s character ultimately disintegrated were left on the cutting room floor.

“I directed because I couldn’t be heard,” said Streisand.