The 32-year-old from Co. Kerry was nominated for an Academy Award for Best Supporting Actress for her role as Leda in The Lost Daughter.
Speaking to Ray D’Arcy on RTE Radio One, Jessie’s musician mum Marina said she missed Jessie’s call when she rang with the news.
“I’m at work, I work in a school as a music teacher and a music therapist so that's what I’ve been doing,” she said.
“It was my son Cillian, Jessie’s brother who lives in France [who told me] he seemed to get the news first.”
“I'd noticed a missed call from Jessie herself so I got back to her within a couple of minutes,” she said.
Marinna said that her daughter is absolutely “bowled over” by the nomination.
“She can't believe it because it’s such an incredible honour and recognition of her work and she doesn't take that lightly or take it for granted in any way.!
"Music was very much part of her life growing up, her dad is also very creative. She was immersed in creativity from a young age,” she said.
Meanwhile, Jessie’s dad Tim paid tribute to fellow actors Ruth Negga and Catriona Balfe who missed out on Oscar nominations.
“We’re delighted, it's a fantastic honour for the filmmakers, but it’s a fantastic honour for the other Irish people that nearly got there as well… Ruth Negga and Caitriona Balfe.”
“It's great that somebody gets the recognition, I won’t say we’re blasé about it, but there's a lot of twists in the road to fame or success and we honour everybody.”
“That keeps her grounded, we're the safety net when things fall apart,” he added.
Reacting to the news of the nomination, Jessie said in a statement: “I am in complete shock!”
“The Lost Daughter is so special to me.”
“To be recognised for anything connected to it is just a wild dream come true. And to gorgeous Olivia Colman and our leader and legend Maggie Gyllenhaal, I’m so lucky to share this ride with you incredible women. Thank you.”
The Lost Daughter follows Leda (played by Oliva Colman, and by Jessie Buckley in flashbacks), who becomes consumed with the relationship between a young mother (Dakota Johnson) and her daughter as she watches them while on the beach.
Unnerved by them, and their extended family, Leda becomes overwhelmed by her own memories of motherhood.
The film, which was adapted from a novel by Elena Ferrante, was directed by Maggie Gyllenhaal.
It also stars Ed Harris, Peter Sarsgaard, Paul Mescal and Dagmara Dominczyk.
The Academy Awards take place on Sunday, 27 March.