Roberts spoke to WSJ Magazine in late February about Nancy Motes' death from a possible drug overdose and the interview was released today.
"It's just heartbreak," she told WSJ, tearing up. "It's only been 20 days. There aren't words to explain what any of us have been through in these last 20 days. It's hour by hour some days, but you just keep looking ahead."
Motes was found dead in Los Angeles on Feb. 9 at the age of 37.
The Oscar winner and half-sister of Motes added, "You don't want anything bad to happen to anyone, but there are so many tragic, painful, inexplicable things in the world. But [as with] any situation of challenge and despair, we must find a way, as a family. It's so hard to formulate a sentence about it outside the weepy huddle of my family."
Roberts, 46, who spoke to the magazine as part of her promotion for her May 25 HBO movie "The Normal Heart," added candid details about her personal life with husband Daniel Moder and her children Hazel and Phinnaeus, 9, and Henry, 5.
"By the time we had kids, I had accomplished things and felt secure about that part of my life," she said. "I was so joyful moving into the family phase of my life in a sincere way."
She also joked that when her twins arrived in 2004, she wanted to be with them as much as possible.
"For a long time they weren't even aware I had a job because I was home so much," she added.