The Olympic swimmer and his professional dance partner were sent home by the judges this week - the midway point of the competition - after landing in the dance-off for the second time, opposite Tilly Ramsay and Nikita Kuzmin.
Jones, 32, tearfully told Peaty: "I was not ready to be in this position today. But looking back, this is you, you have done all of this. None of us expected you to come from the Olympics.
"But what was really nice, after the dance-off, I looked at him and he had tears in his eyes. Someone who’s an absolute unbeatable machine that we see defending his titles for seven years non-stop, being emotional about dancing.
"I really think you deserve a lot more appreciation for what you’ve done and I was not ready for this."
Peaty, 26, competed in the Tokyo Olympic Games in July this year, winning two Gold Medals and setting a World Record for the 100 metre medley relay race, before signing up for the BBC celebrity dance contest.
He was given a standing ovation by his fellow contestants after presenter Tess Daly hailed him as an Olympic hero.
He said: "I have absolutely loved every single challenge. I’ve never had a challenge like this. As an Olympian for 16 years, I’ve pushed my body to places that I never thought it could be pushed. This is just a whole new ballgame and I’ve got so much respect for everyone that dances across the world and to all of these contestants and pros that put themselves on the line every single week, it’s just a great, great experience."
He added: "I just want to say thank you to Katya, everyone behind the scenes, all the judges, wardrobe, make-up artists, hair… absolutely everyone. It's been incredible."
After Peaty and Katya reperformed their Jive, and 19-year-old Ramsay and Nikita Kuzmin danced their Tango a second time, judges Craig Revel Horwood, Motsi Mobuse and Anton du Beke all chose to save Ramsay.
Watch: Adam Peaty says he has forgotten how to swim
But head judge Shirley Ballas revealed: "I would have saved Adam and Katya."
Revel Horwood said: "Firstly, I wouldn’t have put these couples in the bottom. That’s just me personally, but seeing they are there and I’ve got to choose, I’m finding it really difficult tonight and this isn’t like me.
"But for the reason of a better dancer and a better dance-off scenario, I’m going to choose to save Nikita and Tilly."
Mabuse said: "I mean, it has been a tough competition. All the couples have performed really, really well. One of the biggest lessons I’ve ever learned while judging is music is key, and I think the couple for me that was more sound to the music is going to be Tilly and Nikita."
Du Beke said: "Well, this was a great dance off. I’m delighted for both couples performing that well in the dance off. If you have a dance off, you want both people to dance really, really well and they both did.
"I found it so equal I was desperate for something to happen to make me choose and there was a moment in one of the dances that made me decide - and that was Tilly and Nikita."
Ramsay - daughter of TV chef Gordon Ramsay - was third from the bottom with 31/40.
Peaty had admitted he was feeling the strain of being in the public eye following speculation that he "almost kissed" pro partner Katya Jones at the end of their passionate Argentine Tango in Week 4.
Peaty – who has a 13-month-old son with girlfriend Eirianedd Munro – tweeted: "My favourite dance so far. Thank you to everyone who has sent supporting messages! I loved it.
My favourite dance so far 🇦🇷 Thankyou to everyone who has sent supporting messages! I loved it 🙏🏼 To everyone who wants to see what they want, your comments have real life consequences. I will not be overcome or lowered by your gossip. Protect your energy ⚡️🖤 pic.twitter.com/qa8TamcNDY
— Adam Peaty MBE (@adam_peaty) October 17, 2021
"To everyone who wants to see what they want, your comments have real life consequences. I will not be overcome or lowered by your gossip. Protect your energy."
The 26-year-old Olympian – who met Munro when he was training at Loughborough University where she was a student – was shown moving his face close to Jones at the end of their dance on Saturday night as he swept her backwards into a hold, before quickly adjusting his pose.
His girlfriend Munro has already made fun of the speculation that Peaty had been about to kiss Jones on live TV with a video posted on TikTok.
In a parody video she pretended to cry to camera, writing: “Watching your boyfriend almost kiss another woman on live TV.”
Watch: Adam Peaty's girlfriend reacts to that 'almost kiss' on Strictly
She then threw her head back dramatically adding: “Finding out 10 million other people also watched it live.”
During the 2018 series of Strictly, Jones, 32, was pictured kissing her celebrity partner comedian Seann Walsh last year while enjoying a night out between rehearsals.
She and Walsh both publicly apologised but were voted out of the BBC dance contest a week later.
Jones split from her husband, Strictly pro dancer Neil Jones, 39, in August 2019.