Harry, who was 12 when his mother died, also spoke of the sense of loss he and his brother Prince William still feel, a decade after their mother was killed in a high-speed car crash in a Parisian tunnel.
“William and I can separate life into two parts,” he told 500 guests at the Guards Chapel in central London as his elder brother bowed his head in the front row.
“There were those years when we were blessed by the physical presence beside us of both our mother and father and then there are the 10 years since our mother's death.”
William and Harry spent months organising the event, attended by Queen Elizabeth II, Prince Charles, Prime Minister Gordon Brown and Diana's two sisters and brother, plus friends like Sir Elton John who sang at her funeral.
It was the main event to commemorate Diana on the anniversary, although a crowd of her supporters also gathered outside her former home to pay their own tribute.
The 22-year-old prince, who is now an army officer like his brother, said his mother would “always be remembered for her amazing public work”.
“But behind the media glare, to us, just two loving children, she was quite simply the best mother in the world,” he added.
“We would say that wouldn't we? But we miss her.”
He concluded his speech by saying: “She made us and so many other people happy - may this be the way that she is remembered.”
Members of the public were not admitted, but hundreds gathered outside the chapel to listen to the service through loudspeakers.
Harry's address reduced many of them to tears and earned a loud round of applause at the end.
William, 25, read a Bible passage at the ceremony, which featured music by Mozart, Rachmaninov and Faure and concluded with a rendition of the national anthem.
Conspicuous by their absence were Charles's second wife Camilla, Duchess of Cornwall - described by Diana as the third person in her marriage after a long-term affair with Charles - and Mohamed Al Fayed, father of the princess's boyfriend Dodi Fayed who also died in the crash.
Camilla pulled out on Sunday saying she did not want to distract from the proper purpose of the occasion, while Fayed, who insists the couple were killed in an establishment plot, was not invited.
The Egyptian millionaire hosted a two-minute silence at upmarket London department store Harrods, which he owns, attended by about 100 people.
Last year, a report from Lord John Stevens, former head of London's Metropolitan Police, ruled out any conspiracy and said that the crash, which also killed the car's driver Henri Paul, was a “tragic accident”.
William and Harry's girlfriends, Kate Middleton and Chelsy Davy, were also absent from the service.
Diana's death generated an unprecedented outpouring of public grief in Britain.
One million people took to the streets of London for the funeral and some say the episode changed the country.
The tragedy also forced the royal family to present itself as a more open and inclusive institution.
The gates of Diana's home, Kensington Palace in London, were festooned today with flowers and poems left by admirers, a crowd of whom held their own memorial service, led by a retired priest.
Eileen Heathey, 56, from London, said Diana would be remembered for her compassion.
“That's what I remember her for - her caring and understanding,” she said.
"She had a lot of hurt in her own life that made her do what she did."
Flowers also piled up at Althorp, Diana's childhood home and final resting place, which broke with tradition by opening to the public for the anniversary.
Kensington Palace is also hosting an exhibition in her memory, as is London's National Portrait Gallery.
And the BBC is rescreening her funeral in full on a digital channel tomorrow.
Image From Reuters