Sophie, 56, and her husband Prince Edward, 57, spent around an hour visiting his mother on Saturday.
As they left Sophie fought back tears as she spoke to reporters from a Land Rover driven by her husband.
“The Queen has been amazing,” she said.
Police cleared the road as their vehicle left the area as the countess waved to members of the public.
Hundreds of people have travelled to Buckingham Palace and Windsor Castle to lay flowers despite being urged to stay at home.
Floral tributes have been removed to prevent people gathering in line with Covid restrictions.
Prince Andrew, who lives in the grounds of Windsor Castle, also visited his mother on Saturday.
The Queen is said to have been by her husband’s bedside as he passed away on Friday morning.
Buckingham Palace released a statement at midday confirming the duke’s death.
“It is with deep sorrow that Her Majesty The Queen has announced the death of her beloved husband, His Royal Highness The Prince Philip, Duke of Edinburgh,” it said.
“His Royal Highness passed away peacefully this morning at Windsor Castle.
“Further announcements will made in due course.
“The Royal Family join with people around the world in mourning his loss.”
On Saturday, gun salutes were fired across the UK, in Gibraltar to mark the death of the Duke of Edinburgh.
Saluting batteries began firing 41 rounds at one round every minute from midday in cities including London, Edinburgh, Cardiff and Belfast, as well from Royal Navy warships.
In London, the King’s Troop, Royal Horse Artillery, fired 36 horse-drawn guns at a parade ground in Woolwich Barracks.
The duke’s coffin is in a private chapel of worship and will be moved to the nearby Albert Memorial Chapel later today.
It is expected to stay there during seven days of national mourning ahead of the duke’s funeral next Saturday.
Prince Harry is expected to return to the UK for his grandfather’s funeral after speaking with senior members of the Royal Family.
According to the Mirror, Harry has already spoken to his father as well as Princesses Beatrice and Eugenie about coming home.
An insider told the newspaper: “He said he wants to be with everyone and was already making arrangements to come home.”
It is not know if Harry’s wife Meghan, who is heavily pregnant, will travel with him.