"I think it's the best gift we can give our children, is the chance to fail," she said.
Jenna reflected on TODAY with Hoda & Jenna Tuesday about the talk she had with her father after she was cited for possession of alcohol as a minor and using a fake ID to purchase alcohol within a five-week span in 2001 as a University of Texas student during George W. Bush's presidency.
"While we were growing up, I for one had parents that let us fail, let us fall and publicly,'' Jenna said. "And I always say to them now, 'How brave of you,' because it didn't reflect great on them, either."
The incidents made national headlines, and Hoda Kotb joked that she probably reported it on the air during her earlier days with NBC News.
"The first time I had a public failure, I called my dad, and I was crying and I apologized to him," Jenna said. "I got a minor (misdemeanor) in possession of alcohol when I was 19.
"And I felt embarrassed, and I felt really badly for him because I thought this is going to make him look bad."
Her father also surprisingly apologized to her.
"He apologized to me because what we wanted more than anything was to just be normal college kids,'' Jenna said. "So he always would say, 'No, you can be normal.' He also wanted to give us what we wanted, some space and to grow, and also I think he wanted to give us the chance to make mistakes, not so publicly.
"He said, 'I'm sorry. I promised you you could be normal, and this isn't normal.' I think I was probably on the TODAY show (at the time)."
Jenna has also previously opened up on TODAY about a talk she had with her father about alcohol when she was in her early 20s. The elder Bush wrote in his 2010 book "Decision Points" about how he gave up drinking after first lady Laura Bush pushed him to decide whether he wanted to choose alcohol or fatherhood.
"He said, 'I just want you to know that there was a point in my life where I thought like this is interrupting what's beautiful,''' Jenna said. "He just knew that it was interrupting his dreams and interrupting his parenting. I always appreciated it, and I still do."
Hoda agreed that allowing children some space to make their own mistakes can play an important role in parenting.
"I think that's why sometimes having your kids in sports, if they like sports, is such a good thing because it reminds you no matter how hard you try, no matter how much you practice, no matter how much you want to win, sometimes you just don't, and that's life,'' Hoda said.
Jenna, who is now a mother of three children herself, hopes to give her kids the same space she had.
"My parents just ignored us and let us go at it,'' Jenna said. "And then you learn conflict resolution on your own. You learn when the limit is. You learn how to apologize. I just am trying to take a step back."