Anoushka, 34, was nominated in the Best World Music Album category for her solo album Home, a pure Indian classical album. A tribute to her late father Ravi Shankar, the song featured two ragas.
Anoushka, who was nominated in the category for the fifth time, lost it out to Angelique Kidjo for Sings.
The Indian sitarist appeared in great spirits as she took to present at the Grammys in a blue Manish Arora dress.
And I didn't even say anyone's names wrong! Such an honour to be part of this day https://t.co/zv1HYRxVZI? Anoushka Shankar (@ShankarAnoushka) February 15, 2016
Mr Kapadia's Grammy win comes close to the heels of his triumph at the BAFTA awards recently. The 44-year-old director's documentary on late singer Amy Winehouse is also nominated for the Oscars. (Also Read: Anoushka Shankar 'Thrilled' to Present at Grammys 2016)