The 37-year-old, who was slammed by online commenters over the pictures she shared of Princess in December 2015, said she understood why she was criticised.
"You're all right. I’m in the wrong," the mum-of-five said on the Loose Women panel when speaking about what age is appropriate for kids to wear makeup.
"To me that's innocent because she’s copying her mum," Price continued. "But so many people said to me 'Oh my god Katie, think about paedophiles.
"And I thought 'Oh yeah, you're right'. When you say it, I can see it."
Price explained why her daughter was wearing so much makeup in the Instagram photos she shared.
"Princess sees how I pose. She thinks it’s natural," she said. "These pictures were taken when we did panto at Christmas and she just saw her mum doing it.
"I wouldn't let her go to the shops like that."
In the video, Princess said: "By the way, I wanna do my makeup. Not my mum, I do. And anyway, it's none of your beeswax, so oooosh!"
Asked if Peter Andre had strong views on the saga, Price added: "He did after the video. He said she doesn't speak like that. And I said 'Yeah, you're right'."
Price, is also mum to Harvey, 13, Junior, 10, Jett, two, and Bunny, one.