The short clip was filmed at a hotel in London on Saturday night, and shows him singing Queen's hit song with other members of the Canadian delegation that attended the Queen's funeral days later.
The office of the Prime Minister released a statement following the backlash.
"After dinner on Saturday, the Prime Minister joined a small gathering with members of the Canadian delegation, who have come together to pay tribute to the life and service of Her Majesty," his office said in a statement to Toronto Star on Monday.
"Over the past 10 days, the Prime Minister has taken part in various activities to pay his respects for the Queen, and today, the entire delegation is taking part in the state funeral."
Quebec pianist Gregory Charles, who was accompanying the group with the backing music, also released a statement saying the group had been paying "homage" to the Queen.
"Have not seen a video, but I did, with a small group of Canadians, get to spend a few splendid minutes with the PM late on Saturday. And there was a piano in the lobby, and I did play a few UK tunes as a spontaneous homage," he told British media.