Culkin, the younger brother of Home Alone actor Macaulay, said the family will never get over the loss of Dakota, who died aged 29 in 2008 after being hit by a car in Southern California.
"That's the worst thing that's ever happened, and there's no sugar-coating that one," he told the Hollywood Reporter.
"Each one of us handled it very differently. I think everyone was just torn up inside.
"What has it been, 13 years now? Holy shit. That's crazy. Jesus f****** Christ. I accepted at the time that this is going to be forever, and it's never going to be fine. It's always going to be devastating.
"I still weep about it out of nowhere. Something funny she did will pop in the head and make me laugh, and then I'm weeping. Sometimes it's knowing that she's not going to meet my kids and they don't get to have her, and it's hard to describe what she was like."
Culkin, 39, is reprising the role of Roman Roy in HBO's acclaimed drama Succession, which is returning for a third season later this month.
He said a moment in the season premiere featuring a row between Roman and his sister Shiv - played by Australian Sarah Snook - reminded him of his sister.
Snook's character pulls a funny face, a trick Culkin said Dakota, who was also known as Cody, also used to do.
He said: "That's just Cody's move. You could never get one up on her because, even if she was wrong - 'Dur-dur-dur-dur-durrr!' - then she wins the argument. Cody is pretty Roman-y. It's as if Roman were portrayed by Darlene from Roseanne. Darlene Connor as Roman Roy."
Succession season three will begin airing in the UK on October 18.
