The 24-year-old explained that they said she was "too ethnic" to ever be successful.
She told the crowd during a concert at Madison Square Garden last night that her teachers said: "You'll never be the heroine, the blonde, the star. Your hair's too dark. You look too ethnic."
She went on to say that she had replied to them: "What about Liza?" - referencing actress and singer Liza Minelli, who was at the show.
The singer also praised her hometown New York and thanked her fans for making her "brave".
She added: "I used to live 20 blocks from here, so I saw all those names go up on the Marquis, and I always wanted to see my name up in those lights.
"You made me brave, little monsters, and New York made me brave."
