In July last year, Simon catapulted onto the front pages with the shock news that he was having a child with the married New York socialite. The couple went on to welcome baby Eric on Valentine's Day.
"I regret that part," the 54-year-old told the Mirror of the affair, which took place while Lauren was married to Simon's former friend Andrew Silverman. "But then of course you have a baby and you look at the baby and you kinda go, 'This is what happened from it'.
"In this situation you are not going to come out well because of the circumstances. It is not something I am proud of or wanted to happen in terms of hurting anyone.
"It just happened. You have to deal with it and man up to it. You have to accept the responsibility and the criticism."
Life has changed drastically for Simon since he became a first-time father in February. He has gone from living a solitary existence to sharing his West London mansion with Eric, Lauren and dogs Diddly and Squiddly.
"Now the house is full of people, it has become a home rather than a house," he said.
"Everyone said 'it must be turning your life upside down', but I love it. The dogs are mad and Lauren is not exactly the most quiet person in the world."
Someone else fully embracing the change in Simon's life is his mum Julie.
She had given up on having any grandchildren from her famous son prior to the pregnancy announcement last year. And she was particularly emotional the first time she met her little grandson, who was named after her late husband.
"She never thought at my age I would be turning up at Brighton with a grandson called Eric. She would never have predicted it," Simon said.
He also revealed that Lauren was the driving force behind the baby's name.
"We were teasing people about the name being Simon," the X Factor mogul said. "Eric seemed the more obvious choice.
"Even though Lauren had never met my dad she knew my relationship with him was very strong and she felt quite passionately that he should be named after my dad, I thought that was sweet. We told my mum before anyone else."