Storey shared her disappointment while chatting to BBC presenter Abi Clarke moments after her departure on the spin-off show, Strictly: Lights Up.
“We said to each other backstage, you’ve just got to take on board those comments and put them into practice immediately, and so, that’s what we did,” she said.
“I’m also disappointed that I don’t get to bring it on Monday to try and do the same again.”
Dame Sarah Storey and Julian Caillon (left) and Bethany Antonia and Nancy Xu during the results show on Sunday
PA
She also shared a photo of her and partner Caillon on Instagram, writing: ““Thank you for being the best pro I could have ever wished for @julian_caillon you really are a wonderful and fabulous human, and I so loved our time on the show.
“Shorter than we wished for, I will miss not learning a new dance with you tomorrow and trying to put all the tips and feedback into practice. PS, I love your idea of a bike ride.”
Caillon commented on the post: “So proud of you and how much you’ve grown as a dancer!! Have loved spending time together, having a boogie and can’t wait to get some more rides in.”
The couple placed bottom of the leaderboard during Saturday’s Icons Week episode, having scored 21 for their routine.
Judge Craig Revel Horwood said they “dropped the ball a little bit” during the dance, while Shirley Ballas praised their “attitude, character and dramatics”, which she called “a very good start”.
Actor Antonia and her partner Xu placed third from the bottom after scoring 27 for their cha cha to Respect by Aretha Franklin - but had to dance again after the public vote was added.
Horwood, Motsi Mabuse and Anton Du Beke opted to save Antonia, meaning head judge Ballas did not need to use her deciding vote.
The decision divided viewers at home, with some claiming Storey was “let down” by the Icons theme.
“The right person won in that dance off, having said that, Sarah was definitely sabotaged by that stupid theme. Imagine dancing a tango to a jolly pop song. A tango is fierce full of passion, not a happy go lucky dance. The theme let her down,” one wrote on X.
“I’m sorry but I’m calling sabotage. How are you going to give Sarah a Tango and give her a poppy song to dance to? I feel like this theme did them a disservice. Massively,” another added.
Others argued that the right person went home, with one posting: “I really do love Sarah and Julian but Sarah is technically worse than Bethany and that was clear in the dance off.”
The results show also featured a performance from the professional dancers paying tribute to Madonna, reflecting the many different eras of her career.
Country singer Belles, who recorded a duet with Parton earlier this year, sang the hit song Jolene while Amy Dowden and Kai Widdrington danced.
The remaining 12 couples will take to the dancefloor next week, with Australian singer Delta Goodrem set to make a return after receiving a bye this week due to an injury.
Strictly Come Dancing returns at 6.30pm next Saturday on BBC One.