Lily Gladstone Was ‘Really Upset’ That Cate Blanchett Didn't Win an Oscar for Elizabeth (Exclusive)

Lily Gladstone is a Cate Blanchett fan!

In an exclusive interview for PEOPLE's annual Oscar portfolio, Gladstone, 37, opens up about how she was disappointed when Blanchett, 54, lost the Best Actress race at the 1999 Academy Awards, when she was nominated for the biographical period drama Elizabeth.

"I've idolized Cate Blanchett since I was a teenager. When ... she was up for Elizabeth at the Oscars and didn't win, I remember just being really, really upset about that," Gladstone says. "She's my ultimate actress. I think she's the great talent of this generation."

Blanchett, whom Gladstone also describes as having been "so kind" to her on occasions when they have met, was nominated that year alongside Fernanda Montenegro, Meryl Streep, Emily Watson and Gwyneth Paltrow — who won for her role as Viola de Lesseps in Shakespeare in Love.

Amid the awards show circuit these past few months, Gladstone says she has "run into" Blanchett "several times."

"She goes out of her way to support the film," Gladstone adds, referring to Killers of the Flower Moon, for which she is nominated for Best Actress.

As for advice that Blanchett has given her during the many times they have crossed paths, Gladstone reveals, "Her big tip was to keep up on your adaptogenic mushrooms through this whole period, which is great advice."

"That is a very quick, easy, self-care ritual that I can adapt, coming from one of the most brilliant actors alive," she adds.

At this year's ceremony, Gladstone is nominated in her cateogry alongside Annette Bening, Sandra Hüller, Carey Mulligan and Emma Stone.

In Killers of the Flower Moon, Gladstone portrays Mollie Burkhart, a real-life woman who was a member of the Osage Nation.

Mollie's family members, including her mother and sisters, were killed by men over their rights to oil reserves located underneath their reservation in Oklahoma.

The Martin Scorsese movie — which can be streamed on Apple TV+ — also stars Leonardo DiCaprio, Robert De Niro and Jesse Plemons.

Gladstone, who is of Siksikaitsitapi and Niimiipuu heritage, is the first Native American actress to be nominated for an Oscar. She's the fourth Indigenous actress to ever earn a nomination in the category.

Previously, Merle Oberon was the first woman nominated in the category in 1935 for playing Kitty Vane in The Dark Angel. In 2003, Kiwi actress Keisha Castle-Hughes was nominated for playing Paikea, a young girl fighting for the respect of her family in Whale Rider.

Speaking about what she is looking forward to most about this year's Oscars, Gladstone tells PEOPLE, "I think just being there and absorbing the magnitude of how much of an impact this film has made. I'm so excited that I get to share this."

The 96th Academy Awards, hosted by Jimmy Kimmel, will air live on Sunday, March 10, from the Dolby Theatre in Hollywood, California, beginning at 7 p.m. ET.