Andrew Murray, a former JC employee, and his partner, Darren Sarsby, a magician and illusionist, apologised to viewers after the blunder.
It was the first time they had made a mistake on the show, but it scuppered their hopes of victory.
They had been attempting to predict a page number selected in a book during their routine, but guessed it was page 31, when in fact the answer had been 81.
After the performance, BGT judge Simon Cowell said: “It’s ok, because it makes you human.”
But viewers disagreed with his sentiment.
Mr Murray, a 43-year-old father of two from London, and Mr Sarsby, who is from Essex, had thrilled audiences with their spell-binding performances on their route to the final.
Their first audition was seen by more than nine million viewers when it was broadcast on TV in April, and their debut has since been seen by millions more on YouTube.
DNA received just three per cent of the votes from viewers, leaving them last in the 11-act final last night.
The show was won by pianist Tokio Myers, who will now play at the Royal Variety Show.
Jess Robinson failed to reach the final after appearing in the semi-final on Friday night. She had hoped to emulate Francine Lewis, another Jewish impressionist who reached the final round four years ago.
Ms Robinson, from north London, put together a performance including impressions of Shirley Bassey, Tina Turner, Adele and the Queen in her appearance, but did not finish in the top three and failed to progress to the last stage.
