Macchio, 48, also starred in two "Karate" sequels, along with Pat Morita, who died in 2005.
The new version of the flick stars Jaden Smith and Jackie Chan in the roles of karate student and master teacher.
"It's like mixed feelings. At first, I felt old. Number one, you feel old when they start remaking your stuff," Macchio told TV's "Access Hollywood" at the Los Angeles premiere for the new movie Monday night.
"Once I got past the fact that there's a whole new generation, it was more about, 'OK, you can retell this story because it's a beautiful story,'" the actor added. "It's a testament to the legacy that we created that we didn't even know we were creating. I don't look at it as the end of an era and the beginning of a new one. It's not the passing of the torch as much as it is the celebration of a great story."
Macchio went on to say he had no idea when he was making the first "Karate Kid" that the film would become a classic.
"We didn't know what we were doing. We didn't know the magic that was happening and the Pat Morita performance and all the Cobra Kai and 'wax on, wax off' and catching flies with your chopsticks and the crane just became part of everyone's childhood and that's what I'm here celebrating," Macchio said.
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