The 36-year-old from Ireland, who is nominated for best actress Oscar for the film, said she didn't expect the nod, while speaking at London's BFI Southbank on Saturday.
"I don't think you have any idea of an aftermath before you start, never, and if you do, you know that it's going to be the opposite of what you think it's going to be," she said.
"I think we all (the cast) felt like making it was such a special experience, but it's so vulnerable ... that first moment when you share something that has really been such a personal, life-changing experience, it's so vulnerable," she said.
"It's like giving birth, you're like, 'no, my baby', and then, it's okay, but I'm so thrilled and proud that a film like this and a story like this, and protagonists like this can have such an impact, that really it's kind of taken its own course in a way that I didn't know."
She feels the film is a once-in-a-lifetime opportunity.
"I may never do anything like this ever again," she said.
"Sometimes just there's this collision, and this story met me at a point in my life, and ... I feel like there's something about Hamnet, which in my work, was kind of leading me to tell this story at this moment in my life."
Hamnet, directed by Chloe Zhao, tells the story of William Shakespeare's (played by Paul Mescal) wife Agnes Hathaway, played by Buckley, and the couple's reaction to the loss of their son.
The film has broken the record for the most nominations for a female-directed film in Bafta history, with 11.
Asked how she was dealing with her success with the film, Buckley said her baby kept her grounded.
"I had a baby six months ago, so I'm also changing nappies at 3am, and I think it's a gift," she said.
"My work's done, this bit is about sharing it with the world, and the other stuff is something that I guess, going into those rooms and places, I still am in awe that I'm around artists that have inspired me in ways that I couldn't even tell you because I would make an absolute fool of myself."
Buckley, who has also starred in Beast (2017), Women Talking (2022) and The Lost Daughter (2021), has secured a string of trophies including the Golden Globe and Critics' Choice awards for her role as Agnes, for which she is also nominated in the leading actress category at the Baftas.