He thanked the judges for the "extraordinary" way they had whipped up public support in his favour.
The BBC is offering to reimburse anyone who voted for Sergeant on 15 November.
The 64-year-old performed a waltz to the music Come Away With Me with his dance partner Kristina Rihanoff.
I certainly wasn't pushed, Brucie
John Sergeant
Despite Sergeant coming bottom of the score-board three weeks in a row, the voting public had chosen to keep him in the competition.
Explaining his decision to quit earlier in the week, he said winning the competition was a "frightening thought".
He added: "I didn't want that to happen because it would have been a very bittersweet victory."
The BBC has received more than 2,000 complaints about Sergeant's departure since he announced he was quitting the show.
The programme's co-host Bruce Forsyth said he felt "very sorry" for Sergeant.
"He was put in the most awkward position, looking at the other dancers and knowing they were better than him. He must have felt guilty in a way."
On Saturday, Sergeant told the host: "I certainly wasn't pushed, Brucie."
Perfect score
Strictly judge Arlene Phillips said: "I'm always sad if a contestant leaves of choice, because you are always expecting to let the public vote them in or out - but John is his own person and he has his own reasons for doing this."
She added Sergeant had provided many "funny, funny moments".
Jodie Kidd, Tom Chambers, Christine Bleakley, Austin Healey, Lisa Snowdon and Rachel Stevens remain in the competition.
Stevens and her partner Vincent Simone scored the first perfect score of the series, with four 10s from the judges.
The BBC is offering to reimburse anyone who voted for Sergeant on 15 November.
The 64-year-old performed a waltz to the music Come Away With Me with his dance partner Kristina Rihanoff.
I certainly wasn't pushed, Brucie
John Sergeant
Despite Sergeant coming bottom of the score-board three weeks in a row, the voting public had chosen to keep him in the competition.
Explaining his decision to quit earlier in the week, he said winning the competition was a "frightening thought".
He added: "I didn't want that to happen because it would have been a very bittersweet victory."
The BBC has received more than 2,000 complaints about Sergeant's departure since he announced he was quitting the show.
The programme's co-host Bruce Forsyth said he felt "very sorry" for Sergeant.
"He was put in the most awkward position, looking at the other dancers and knowing they were better than him. He must have felt guilty in a way."
On Saturday, Sergeant told the host: "I certainly wasn't pushed, Brucie."
Perfect score
Strictly judge Arlene Phillips said: "I'm always sad if a contestant leaves of choice, because you are always expecting to let the public vote them in or out - but John is his own person and he has his own reasons for doing this."
She added Sergeant had provided many "funny, funny moments".
Jodie Kidd, Tom Chambers, Christine Bleakley, Austin Healey, Lisa Snowdon and Rachel Stevens remain in the competition.
Stevens and her partner Vincent Simone scored the first perfect score of the series, with four 10s from the judges.