09/28/2012 at 12:40 PM EDT
Opening up for the first time since his marriage collapsed
with the revelation that he fathered a child with a housekeeper, Arnold Schwarzenegger acknowledges how badly he hurt wife Maria Shriver and their family.
Promoting his upcoming book
on Sunday night's 60 Minutes
on CBS, the action star was asked by correspondent Lesley Sthal, "Was this just the most unbelievable act of betrayal to Maria?"
"I think it was the stupidest thing I've done in the whole relationship," Schwarzenegger, 65, replies. "It was terrible. I inflicted tremendous pain on Maria and unbelievable pain on the kids."
In Total Recall: My Unbelievably True Life Story,
Schwarzenegger writes about the affair with Mildred Baena that produced a son
, Joseph, now a teenager, and reveals another affair during his relationship with Shriver. He says Shriver, who filed for divorce in May 2011
, has not read the book.
"She knows that it's about my whole life and that I would not write a book and kind of leave out that part and make people feel like, 'Well, wait a minute. Are we just getting a book about his success stories and not talk about his failures?'" he says. "I wanted to write a book about me."
The full interview airs Sunday at 7:00 p.m. on CBS.