Her time with Dean Sheremet was "great" but LeAnn Rimes says the two ultimately couldn't make their marriage work – and she's not proud of how she ended it.

"I understand why people are disappointed in me, especially since I grew up as America's sweetheart," the country singer, 28, tells the October issue of Shape, on newsstands Sept. 20. "I think any relationship is hard to get out of, and I don't think the way I did it was right."

Rimes, whose nearly eight-year marriage to Sheremet fell apart as she began seeing actor Eddie Cibrian. She told our friends over @PEOPLE in June that she regretted her actions, saying "I did one of the most selfish things that I possibly could do, in hurting someone else,"

She also points to getting married young as the reason for the split. "It wasn't a fulfilling marriage for either of us," she tells Shape. "As we got older, we grew apart."

Still, Rimes knows that "there are lessons in it for me to learn" and says she's figured out what she calls "the most important thing," which is "cultivating strength from rough situations."

"After going through this," says Rimes, who finalized her divorce in December and has since moved in with Cibrian, "I know I can face anything."