The actor was deeply moved by the honor while speaking with ET backstage at the show.
After delivering a heartfelt acceptance speech on stage at the Barker Hangar in Santa Monica, California, on Sunday -- when he earned the award for Outstanding Performance by a Male Actor for his role in King Richard -- Smith opened up to ET's Nischelle Turner backstage and reflected on the honor.
"I'm here tonight with Saniyya [Sidney] and Demi [Singleton], the girls who play Venus and Serena, and Aunjanue Ellis, and Venus is here with her sister Isha, who's an executive producer," Smith said, as he began to choke up. "It's all of these, all of these Black women that I get to protect and shine a light on, you know, across the generations."
Smith, after taking a moment to compose himself, explained he feels "such a responsibility" to them to tell their story.
In the biopic, Smith portrays Richard Williams, the father of tennis icons Venus and Serena Williams, who has a singular vision of helping his young daughters become legends on the court.
When asked what he feels about the real-life figure he portrays in the film, Smith said, "It's just like I get him. I get him."
"You know, [he's] that post-World War II Black man in America with a dream and everyone tells you, 'You're crazy,' you know?" Smith shared. "My father was that guy, and he just [has] these big dreams and no support at all, but you do it anyway."
Smith also reflected on the standing ovation he received from fellow star Denzel Washington after it was revealed that Smith had won the award.
"Me and Denzel have had some moments over the past 15 years. He's always been a mentor for me, and he's seen a whole lot of iterations of Will Smith," he explained. "Like, Denzel's always one of my first calls when stuff's not going right. He's given me critical advice at really critical moments."
"[Tonight], he just hugged me and said, 'This is your year,' and he said, 'I'm so proud of the man you've become,'" Smith added. "He grabbed a weight off of [my] shoulders and said, 'You got it.'"
Check out the video below for more from the celebrated actor's big night at the 2022 SAG Awards.
Helen Mirren Jokes She's SAG Awards 'Homecoming Queen' as She Receives Lifetime Achievement Award