In an interview with PEOPLE, the 55-year-old "Gilmore Girls" star revealed they could not see eye-to-eye about their values which ultimately led to their split.
"I think part of all the positives of having known each other for a really long time were there," Graham explained. "And one of the negatives of that is we almost came into a relationship as people in their 40s without asking any of the questions people in their 40s should be asking."
The "Parenthood" star revealed that when she had met Krause for the first time in 1995, the pair "had such a good time together" that they neglected to talk about their differences.
"I didn't maybe ask some fundamental questions about "What are your values and what do you envision?' and those more grown-up things," she explained. "And then they just caught up with us."
Lauren and Peter began their relationship back in 2010 after playing siblings on "Parenthood." The two were together for more than a decade and parted ways some time last year.
Graham has channeled her heartbreak into writing a memoir titled, "Have I Told You This Already? Stories I Don’t Want to Forget to Remember” she expects to release on Nov. 15.
"I just was not going to let [the breakup] flatten me," she told the outlet. "I was like, 'OK, well, look at all the good stuff I have, and look at all the good times,' and 'I'm going to write this book.' Thank goodness I have these outlets and these stories to tell."
Graham said she was "resilient because I just always have been" and recalled learning to "take your knocks and don't complain. That's how I was always raised."
"I'm less on the run," she continued. She noted that taking time has helped her heal her wounds, "Any pain still really has its moments. I was a contributor in the life of his child, and so we're connected. And yes, I'm in a better place, but it's still just a shame. It's just sad to me."
While Graham confessed she's open to finding love again, she won't be looking to join any dating apps anytime soon. You don't get the sense really of what your actual chemistry is," she said. "You're just getting what game they're playing or what method they use. It's just not the full picture."