Ralph Macchio Talks 'Embracing' “Karate Kid” Nostalgia — and Making a Cameo in a New Coldplay Video

The ‘Cobra Kai’ actor stars in the band’s latest video for their song inspired by his 1984 film

Ralph Macchio says there’s nothing to do but “embrace” nostalgia for The Karate Kid.

The actor, 63, was a guest on the Wednesday, Nov. 20, episode of Jimmy Kimmel Live, where he told the host all about performing opposite Robert De Niro and Burt Young in the 1986 Broadway play Cuba and His Teddy Bear, two years after appearing in The Karate Kid.

Macchio recalled both Joe Pesci, with whom he would later star in My Cousin Vinny, and Mike Tyson coming to see the play.

“Mike Tyson’s first Broadway show was me and De Niro,” Macchio said. “And I’ve run into him once or twice since and he always says, ‘I remember that was my first Broadway show, Cuba and His Teddy Bear.’ And he never forgets it.”

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 celebrity news to compelling human interest stories. 

Macchio also recalled an even more memorable performance of Cuba and His Teddy Bear. “We did one performance at Rikers Island,” he said of the New York City prison island. “I was a little nervous about it, to be at Rikers. Maybe a lot of Bob De Niro’s friends were there, maybe Burt Young’s family was there,” he joked.

“They were cheering De Niro when he first came out,” Macchio recalled. “Like worshipping Travis Bickle from Taxi Driver.”

During one scene in which Macchio was involved in a physical struggle with another actor, he said the Rikers crowd was calling out for him to perform his signature moves from The Karate Kid. “They were just like, ‘Sweep the leg! Come on!’ ” he said. “They just wanted to see the crane.”

Macchio admitted that to this day, he still hears people reference the film’s “sweep the leg” line all the time. Kimmel suggested that might be both a blessing and a curse.

“Not now,” Macchio said. “But maybe there were years that maybe I thought of it that way. Now, when I get 8- and 10-year-old kids that are inspired by these characters and the themes of that movie, there’s only one thing to do: Embrace it.”

Related: Ralph Macchio Receives Star on Hollywood Walk of Fame as His Cobra Kai Costars Praise His 'Old-Fashioned Class'

Macchio certainly has embraced the Karate Kid legacy. Since 2018, he’s starred in spin-off series Cobra Kai, which just dropped the second half of its final season on Netflix earlier this month. And next year, he’ll star opposite Jackie Chan in the franchise’s sixth film, Karate Kid: Legends.

He also recently teamed up with a particularly noteworthy fan, Coldplay frontman Chris Martin, to appear in the video for the band’s new single, aptly titled “The Karate Kid.”

Macchio explained that his son showed him a clip of Martin performing the song, which appears on the deluxe “Full Moon Edition” of Coldplay’s latest album Moon Music. “I thought it was a beautiful song, so I posted it,” he said. “Next day, I’m getting a FaceTime from Chris Martin — never met him in my life.”

The singer pitched Macchio his idea for the video, which filmed in Australia and finds the actor lip syncing to Coldplay’s song in various locations before appearing with Martin live onstage.

Related: Meet the Real-Life Loves of Netflix’s Cobra Kai Cast (Including the Couple Who Played On-Screen Rivals!)

When Kimmel asked whether the two had kept in touch, the actor admitted that Martin “FaceTimed me yesterday … I just couldn’t talk to him and then he FaceTimed me again, and frankly, I thought this was one-and-done. But, you know, he’s a little annoying.”

The camera then cut to Martin sitting in the studio audience wearing a Karate Kid-esque headband.

“You see what I’m talkin’ about?” Macchio joked. “Listen, he’s a talented kid. I think he’s fantastic.”

Macchio added that a lot of people mistakenly thought Coldplay’s new video was connected to the upcoming Karate Kid film. “A lot of people thought that’s what it was for,” he said. But, he said, the film just “inspired some kid named Chris Martin at 7 years old, and here we are. It’s awesome.”