In a public message to his ex and their son, the swimmer wrote: "I’m sorry for letting you down."
He and Katya Jones have both previously dismissed the "gossip" that came after their Argentine Tango routine.
"She’s got her thoughts and I’ve got mine, and mine is the most important one to me."
Strictly Come Dancing Addresses Katya Jones' Supposed 'Backstage Meltdown': 'Emotions Often Run High'
Katya and Adam Peaty became the latest Strictly pairing to leave the competition over the weekend.
The Olympic swimmer reflected on his Strictly journey during an interview on It Takes Two.
Caroline Peaty claimed the "judging is not consistent or fair" and said she was "not buying the public vote".
"We all have to wear a piece of armour to get the job done and it wasn’t until this week that I knew I could let it go."
One of the series' most talked-about pairings has been eliminated from the competition.
She and Kai Widdrington got glowing reviews for their performance, but the judges still failed to give them a perfect score.
"I am trying to lay it to rest now as I am tired."