Kapadia, who has already won the Golden Globe and Bafta awards for the documentary, paid tribute to Winehouse, who died in 2011 following a battle with drug and alcohol that was gleefully captured by tabloids.
"Really, this film is all about Amy, this is all about showing the world who she really was: not her tabloid persona, the beautiful girl, the amazing soul, funny, intelligent, witty, someone special, someone who needed looking after. We just wanted to make a film to show the world who she really was," Kapadia said while accepting his Oscar trophy.
"...This is for the fans, Amy's fans who loved her through thick and thin, that's all she ever really needed," Gay-Rees said.
Kapadia's documentary saw off competition from "Cartel Land", "The Look of Silence", "What Happened Miss Simone?", "Winter on Fire: Ukraine's Fight for Freedom".
The film has been critics favourite since making its premiere at the Cannes Film Festival last year. Though the singer's father Mitch distanced himself from the documentary, calling it a disappointment.
Kapadia, 44, is known for directing "Senna" in 2012 and Irrfan Khan-starrer "The Warrior" in 2003.