Cillian Murphy Thanks His Wife and Kids for 'Putting Up with Me' as He Accepts Award for Oppenheimer

Award season is off to a winning start for Cillian Murphy.

The Oppenheimer actor, 47, was honored with the Desert Palm Achievement Award, Actor, on Thursday during the Palm Springs International Film Awards.

In his speech, after being introduced by costar Robert Downey Jr., Murphy thanked his family — his wife of nearly 20 years, Yvonne McGuinness, and their two sons Malachy, 18, and Aran, 16 — acknowledging that "because I don't ever really get to do this too often, I want to say thanks to my family."

"Two-thirds of them are sitting down there. We had to leave one of them at home doing exams," said the Irish actor. "But just thanks for putting up with me — putting up with the half me and the shadow me and the absent me, the remains of me when I'm doing a film like this or work in general."

"You're always there. I love it. So thanks, guys," he added.

Never miss a story — sign up for PEOPLE's free daily newsletter to stay up-to-date on the best of what PEOPLE has to offer, from juicy celebrity news to compelling human-interest stories.

In a press release, Palm Springs International Film Festival Chairman Nachhattar Singh Chandi called Murphy's performance a "career-best," praising his "stunning portrayal of J. Robert Oppenheimer as a conflicted scientist leading the Manhattan Project to produce the world’s first atomic bomb."

Like many who have seen Oppenheimer, Downey was floored with Murphy's transformative performance as the physicist who led the U.S. effort to create an atomic bomb during World War II.

Speaking with PEOPLE last summer, the 58-year-old said of his costar, "I have never witnessed a greater sacrifice by a lead actor in my career."

Downey, who plays Atomic Energy Commission chairman Lewis Strauss in the film, said he was impressed by Murphy's "commitment" to the massive undertaking of leading director Christopher Nolan's three-hour epic.

"He knew it was going to be a behemoth ask when Chris called him. But I think he also had the humility that is required to survive playing a role like this," added Downey.

"We'd be like, 'Hey, we got a three-day weekend. Maybe we'll go antiquing in Santa Fe. What are you going to do?' 'Oh, I have to learn 30,000 words of Dutch. Have a nice time.' But that's the nature of the ask," Downey explained.

Florence Pugh, who shares most of her scenes with Murphy as Jean Tatlock, one of the loves of Oppenheimer's life, offered further praise to the Peaky Blinders actor.

"Chris had one of the most incredible leads in Cillian," Pugh, 28, told PEOPLE. "He is an actor that I have been watching for quite some time and have been desperate to work with for ages. You’d have to be mad to say no. It was truly one of the best experiences that I’ve had."

"Working with him was hugely impressive," she continued. "Every single day he shows up knowing every single possible way, intonation, inflection of how to bring this character to life."

"That was hugely impressive to me. There's a reason why he is one of the greats," Pugh added.

Oppenheimer is now available on demand.