"I can't believe we just won Best Original Music at BAFTAs. I wish so much I was there but am at the Grammy's to show them our love as well. We made a film about music. This means the world to me," said Gaga who is due to perform at the Grammy Awards.
The "Poker face" hitmaker appears opposite actor Bradley Cooper in the film.
She thanked all her fans, and wrote: 'We wouldn't be here without you."
"A Star Is Born" is Cooper's directorial debut. In the film, he plays a famous country singer and Gaga essays a rising music star.