"There were moments reading the script that I thought, 'WOW, okay!' " the actress, 24, tells Company magazine's February issue and digital edition. "It's the most private thing anyone can do, but being an actress can make you feel vulnerable."
She adds: "My grandparents watch the show. I don't know why I was so concerned, though. They have been alive for virtually 90 years, so who am I to presume that sex never existed before me?"
Girls was a huge hit at Sunday's Golden Globe Awards, winning best comedy and best actress in a comedy for Lena Dunham. Williams plays Dunham's sidekick and best friend, a character who seems responsible at first, though her insecurities soon become clear.
"We're really different," Williams says of she and Marnie. "I've known I wanted to be an actress since I was 4, but Marnie still has no idea what she wants. But I'm so in her corner, even when she's wrong."
She adds: "In season two, Marnie goes through some real downs. I was shocked at how emotionally drained I felt from that."
Asked what makes Girls so special, Williams tells the magazine (which offers behind-the-scenes footage of her cover shoot") that the show captures the zeitgest for many young people these days.
"There is nothing alienating or too hipster about it," she says. "We're not dating handsome boys. They're weird. We don't have jobs you dream about. In fact, not all of us have jobs. It feels accessible. And the relationship between the girls is brilliant. It's like a digital time capsule – people will watch it in 20 years time, and it will sum up a certain generation."
Williams says she's dealing with her newfound fame mostly by not Googling herself, and shrugs off criticism that she got a head start in the business because she's the daughter of NBC newsman Brian Williams.
"At the end of the day, even if all these wonderful doors are open for you, you have to stride through them," she says.