As Obama was saying, "To her majesty the queen, the vitality of the special relationship between our peoples," the band started playing Britain's national anthem.
Some people wondered if that was the band's mistake, but etiquette experts say standing up and saying "the queen" is a standard cue for the anthem.
On Wednesday, he made light of the situation.
Obama told Deputy Prime Minister Nick Clegg as they settled in for a meeting that the band effectively provided a soundtrack for his closing passage.
"It was like out of the movies, where the sound effect kind of comes in," Obama said.
Clegg, who was a guest at the dinner, told Obama the music had added "a crescendo" to his words.
Royal protocol expert William Hanson said the blame should really be placed on the president's staff because it's their job to make sure he gets briefed on points of etiquette.
The Associated Press contributed to this story.