The 30-year-old batsman announced Tuesday he had been left out of the Twenty20 [ Images ] and One-Day International squads for this month's series against Pakistan in a Twitter message that also included an expletive.
"It came out in a way I didn't want it to come out," Pietersen told Surrey TV on Wednesday.
"It wasn't meant for the public domain. I apologise for it entering the public domain and I also want to apologise for the language I used."
"What he did on his Twitter account was totally wrong," Vaughan told BBC radio. "I think that's something Kevin will regret for a long time."
The England and Wales Cricket Board said they omitted Pietersen, a member of the Twenty20 World Cup-winning side this year and voted player of that tournament, so he could try to regain lost form in county cricket.
The right-hander hit 38 in 33 balls on his debut for new county Surrey in a 40-over match against Worcestershire on Wednesday.