In the statement, released a day after the news of their divorce first broke, they wrote, "Divorce might make one feel like a failure, but eventually you start to find grace in the idea that life goes on."
Barrymore elaborated on the comment, explaining to Handler that there is a big difference between breaking up with someone you've been dating and ending your marriage.
"When you break up with somebody, you're like, 'Yeah, that didn't work,' [but] when you get divorced you're like, 'I'm the biggest failure. This is the biggest failure,'" Barrymore shared. "It's so shameful and hard to actually go through that, even privately."
It was Barrymore's first talk show interview since the split and the 41-year-old "Blended" star seemed excited to open up to Handler about the subject of her tumultuous love life.
"It's a tough time. It's a hard thing to go through. It's like your being put on a cheese grater and every second, going, 'Ah! This wasn't the plan!'" the actress explained.
"There has been this really nice feeling of something very fluid and positive and the opposite of how I felt inside," Barrymore said. "Everyone has just been so cool and chill and nice about everything that it quelled by own fears and demons about how we sort of have to go through things in life."
While Barrymore said that she's come to terms with the split, she balked at the idea of re-entering the dating world -- especially in the age of hook-up apps and dating apps. "What I do want is girlfriend time."
Barrymore and Kopelman, who tied the knot in June 2012, officially called it quits in April, however a source tells ET that talk of separation has been ongoing since September. The couple has two daughters, 3-year-old Olive and 2-year-old Frankie.