Jen Juneau is a digital news writer for PEOPLE since 2016.

Austin Butler had a special bond with the late Lisa Marie Presley.

Speaking with PEOPLE on Monday at the 95th annual Oscar nominees luncheon in Beverly Hills, California, the Elvis actor said he and Lisa Marie "bonded very, very fast."

"And all those special moments of just getting to share life with her, I'll treasure that forever," adds Butler, 31.

Lisa Marie died unexpectedly at the age of 54 last month, shortly after being hospitalized for a suspected cardiac arrest.

Remembering the daughter of Elvis Presley as "such an honest person," Butler says, "There was no filter of how she felt. And she really opened her heart to me very quickly."

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Butler recalled during the Jan. 30 episode of The Tonight Show Starring Jimmy Fallon that, before becoming acquainted with Lisa Marie, he'd "never had an experience where I met somebody and felt an immediate depth of relationship with them."

"She's a person who didn't have anything to prove and wouldn't open up to anybody and she opened up to me," he added. "We got so close so fast and it's just devastating."

"It's weird in moments like this because it's so bittersweet," Butler continued about the emotional contrast of having to promote Elvis — for which he recently received an Academy Award nomination for Best Actor — at the same time as mourning Lisa Marie.

"So much great stuff is happening, but I'm just devastated for her family. And for her to not be here celebrating with us, you know..." he added.

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"I'm happy she got to see you," host Jimmy Fallon said in reply.

"Yeah, I'm happy I got to be with her at the (Golden) Globes — I'll never forget that for the rest of my life," said Butler, who won best actor in a drama for his performance in Baz Luhrmann's movie at the Jan. 10 award show.

On Jan. 24, Butler called in to Today with Hoda and Jenna shortly after the Oscar nominations, which came just over a week after the death of Lisa Marie.

"It's sort of a bittersweet moment right now because I think of how much I wish she was here right now to get to celebrate with me," the actor said. "It's the same thing I feel with Elvis; I wish that they could see these moments, you know?"

He added, "It's just sort of strange to celebrate at a time of such deep grief. But I sort of think of it as a way to honor her. This is for her."

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