The Olympic swimmer sparked speculation that he "almost kissed" pro partner Katya Jones at the end of their passionate Argentine Tango performance on Saturday night's show.
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.
Watch: Who is Strictly's Adam Peaty?
"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.
Watch: Adam Peaty's girlfriend reacts to that 'almost kiss' on Strictly
In a parody video she pretended to cry to camera, writing: “Watching your boyfriend almost kiss another woman on live TV.”
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.
The show is known for relationships developing between contestants and dancers, with 2018 winner Stacey Dooley getting together with her partner Kevin Clifton in one of the most famous Strictly romances.
Dancer Gorka Marquez has a daughter with Hollyoaks star Gemma Atkinson, who he met when she took part in the show, and Flavia Cacace married EastEnders star Jimi Mistry after they were paired on the show in 2010.
Countdown's Rachel Riley split from her husband of just one year, Jamie Gilbert, months after completing 2013’s Strictly.
She is now married to her dance partner Pasha Kovalev and they are expecting their second child together.
And singer Sophie Ellis-Bextor recently revealed that taking part in the show affected her marriage with musician Richard Jones.
Watch: How Sophie Ellis-Bextor disco-ed her way through lockdown