Kate dedicated a Christmas carol service, which took place on December 15 at Westminster Abbey, to the late monarch.
She made the comments during a recorded introductory message this month amid final preparations for the service, which was attended by more than 1,800 people.
It was filmed and will air on Christmas Eve on ITV, hours after the final part of the Duke and Duchess of Sussex’s controversial documentary dropped on Netflix.
Kate was joined by many members of the extended royal family, including the Prince of Wales and their children, Prince George and Princess Charlotte, and King Charles and Queen Consort Camilla.
Introducing the programme, Kate, who led the service with support from the Royal Foundation, said she was “thrilled” to return to the abbey for a second year.
UK royal family attends Westminster Abbey Christmas carol service - in pictures
“This Christmas will be our first without Her late Majesty Queen Elizabeth," she said.
“Her Majesty held Christmas close to her heart, as a time that brought people together and reminded us of the importance of faith, friendship and family, and to show empathy and compassion.
“This year, we’ve invited hundreds of inspiring individuals to the service.
“Those who showcase the power of connectedness and community values, allowing us to continue Her Majesty’s tradition of recognising and thanking those who have gone above and beyond to support others.
“Her Majesty leaves with us an incredible legacy and one that has deeply inspired many of us.”
Kate, Princess of Wales fashion in Boston - in pictures
Kate dedicated the service to the queen and to “all those who are sadly no longer with us”.
“So, whilst Christmas will feel very different this year, we can still remember the memories and traditions we shared," she said.
“Take time to slow down and celebrate with family and friends all the wonderful things that make Christmas so special.”
Hamza Taouzzale, the Lord Mayor of Westminster, who can be seen in full regalia in the video, told The National he had not known that he'd be making an appearance in it.
"I only learned about it when some friends told me soon after it came out. It’s such a lovely surprise," Mr Taouzzale said. "This has been a truly amazing year. If you had said to me in January, some of the things that I’ve done these past few months, I really wouldn’t have believed you.
"But being made Lord Mayor in May, following Labour’s victory in the local elections, has opened up a world that a young person from a Lisson Green council estate couldn’t have imagined possible.
“So, from attending the many community and official parties celebrating Her Majesty The Queen’s Jubilee to representing the people of the city at Westminster Abbey for her funeral a few months later, it has been a fantastic and humbling experience. And now I’ve appeared in the Prince and Princess of Wales’s video for the #TogetherAtChristmas carol service, it is just the icing on the cake. It all feels like a dream.”
The broadcast will also show Inna Hryhorovych, headmistress of St Mary’s Ukrainian School in London, receiving a letter from Kate thanking her for the care she provides to families and children attending the school amid the conflict in their home nation.
In the letter, dated November 18, Kate praises the school as a “lifeline for the whole community” and said she had been struck by their “courage and sense of togetherness during such a challenging time”.
She invited Ms Hryhorovych and the school choir to sing a carol at the service.
UK royals get into the festive spirit at Westminster Abbey Christmas carols service - video
Among the performers were the Westminster Abbey choir, singer Craig David, and Alfie Boe and Melanie C who sang a duet, while Prince William and Dame Kristin Scott Thomas delivered readings.
A Christmas tree in the abbey was decorated with small Paddington Bear decorations, a nod to the late queen’s famous sketch, while guests were greeted with flakes from a snow machine as they arrived.
Narrated by Catherine Zeta-Jones, Royal Carols: Together At Christmas will be broadcast at 7pm on Christmas Eve on ITV1.