"All this controversy makes me sad," Carini told Italian newspaper Gazzetta dello Sport.
"I'm sorry for my opponent, too. If the IOC said she can fight, I respect that decision."
Carini, also 25, said abandoning the fight had been a mature step to take, but she expressed regret at not shaking hands with Khelif afterwards.
"It wasn't something I intended to do," Carini said. "Actually, I want to apologise to her and everyone else. I was angry because my Olympics had gone up in smoke."
She added that if she met Khelif again, she would "embrace her".