"That's just not me. What happened is not who I am, period," the country star, 28, tells ABC's Robin Roberts of the affair with her Northern Lights costar in a special titled All Access Nashville, airing Wednesday night.
But Rimes isn't dwelling on the past. "I do know how much I love him," she says. "So, I've always said I don't live my life with regret. I can't."
Rimes and Cibrian, 37, were both married when they began their affair, and Rimes says now that their situation wasn't that unusual. "It happens every day to so many people," she says. "You had two couples whose marriages didn't work who really stumbled upon each other and fell in love."
The singer has been called everything from a homewrecker to a stalker, and says she's resigned to the idea that some people will never get over her infidelity. "Nothing I'm going to say is going to change it," she says. "I do know that, and I have accepted that."
Cibrian echoes Rimes's sentiments. "The truth is that we're human beings," he says. "We make mistakes and we learn from them, but we're human. We fell in love."
Away from the spotlight, though, Rimes says her love with Cibrian has blossomed. "We're really happy in what we feel privately," she says.