The 56-year-old and Lauren, 38, got together in 2013, allegedly while she was still in a relationship with ex-husband Andrew Silverman.
But Simon and Lauren’s romance was revealed when she discovered she was pregnant with their son Eric in the July.
Speaking to Event magazine, the X Factor boss said: “I’m not proud of the circumstances, I can’t hold my head up about it.”
But, although Lauren’s pregnancy was not planned, Simon admitted he felt an instant connection with his unborn baby.
He continued: “This was not something I planned. But I remember going to the first scan with Lauren.
“I called him Tad because he looked like a tadpole. Something just kicked in. I felt unbelievably protective of both of them. I just absolutely want him. I just hadn’t known that before.”
It’s well-known that Simon has never changed a nappy, but he insisted he and Eric have an unbreakable bond.
“I adore my son,” Simon said. “We make each other laugh. We play with the dogs. I’ve taught him to share, to say please and thank you. Whatever he has he offers it to me.”