In his 40-minute eulogy, the singer's father, Mitch Winehouse spoke of how happy his daughter had been lately, and that she was off drugs and had been trying hard to overcome her alcoholism.
He ended movingly with the words: "Goodnight, my angel, sleep tight. Mummy and Daddy love you ever so much."
Amy's spokesman Chris Goodman was quoted by the Daily Mail as saying: "Mitch was funny, he told some great stories from her childhood.
"It was a celebration. He stressed many times that she had been more content than she had been in years. Mitch paid tribute to a lot of people from Amy's life."
Many of those people were there at the private service in Edgwarebury Cemetery in Edgeware, north London.
In addition to family, mourners included close friend Kelly Osbourne, boyfriend Reg Traviss, producer and DJ Mark Ronson, and goddaughter Dionne Bromfield.
Prayers were said in English and Hebrew, and a rendition of Amy's favourite song, So Far Away by Carole King, brought the service to a close.
After the service, Amy's body was taken to the Golders Green crematorium.
The 27-year-old was found dead at her home in Camden, North London, on Saturday. A post-mortem was carried out on Monday but did not establish the cause of her death.