"I see mean stuff every day; when I look at Twitter I scroll with one eye open and one closed," she told The Edit magazine.
"That particular day, it was just one of the things I saw. I kept scrolling and then I was like, 'Wait a minute, did she just say that?' I went back and I thought, 'Well, this isn't unhealthy paranoia, this is absolutely conscious.
"This was a choice. She, not subtly at all, said that my children are not my children."
After reading the comments, the former Sex and the City actress then famously responded with a series of angry tweets.
"Your anonymity doesn't diminish your outrageous and vulgar tweet," she wrote. "And your deletion only reveals your cowardice.
"I'm certain there isn't a woman on this planet who would support your specific kind of cruelty. No apology, no explanation," she continued.
In the interview, Sarah Jessica also talked about the recent death of fashion designer L'Wren Scott, who she counted as a friend.
"I feel so sad about L'Wren," she said. "I have friends who struggle for no good reason; incredibly talented people who have to fight for attention."
The actress, who has recently turned her hand to designing with a shoe collection, has newfound respect for her fellow designers.
"My heart goes out to designers," she said. "The expectations, the demands they put on themselves. They put everything on the line. It takes fortitude to survive it."