The EastEnders actress lost her place in the BBC contest after falling into the bottom two with Holly Valance and Artem Chigvintsev.
Dobson danced the cha cha cha with Strictly professional Brendan Cole after her regular partner Robin Windsor was forced out with a foot infection.
On her absent companion, Dobson said: "He made this the most humorous, enjoyable, fun, wonderful learning experience you could ever imagine. Thank you so much."
She added to hosts Tess Daly and Claudia Winkleman: "Can I just say thank you to Brendan too, because without him I wouldn't have done this week… thank you."
Before taking her final dance, Dobson was surprised by a phone call from Windsor himself, who described the 62-year-old as "absolutely incredible".
"It has been a pleasure to work with you," he continued. "You have been one of the most enthusiastic and hard-working people I've ever, ever, ever met. I'm going to miss you dearly."
It has been announced that next week's quarter-final will have a 'movie night' theme.
Strictly Come Dancing returns Saturday, December 3 at 7pm on BBC One.
> Anita Dobson: 'I want to stay on Strictly Come Dancing forever'
Watch Anita Dobson on Strictly Come Dancing below: