Speaking at the PEOPLE & Entertainment Weekly Red Carpet Live pre-show, the actor, 76, opened up about the new era in his career.
"I am relaxed," the Barry star said, "I can take it in, I'm not so worried."
With his first acting credits dating back to 1964, Winkler said it's funny to see his fans' age by what they recognize him by. "Happy Days, Scream, Waterboy, Parks & Rec, Arrested Development and now Barry," he said, listing a few of his hit shows and movies.
Winkler is nominated for the third time for his role as Gene Cousineau in Barry in the outstanding supporting actor in a comedy series category. Winkler received nods for his role in the show in 2018 and 2019. In 2018, he took home the award.
"I have the same tie that I had in 2018," he said, adding it was his son's idea. "I'm excited, I'm a little nervous."
Prior to his time in Barry, Winkler's last Emmy nomination was in 2000 for his acting in ABC's The Practice. The actor has received eight nominations throughout his career.
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Also on the carpet, Winkler talked about what made Barry a special project. "Two things: Bill Hader, Alec Berg," he said. "So you know it comes from great bones, like when you go and see a house, and it has great bones, so the auspice already is wonderful, it's written really well, and then I'm so happy I was invited."
When he received this year's nod, Winkler released a statement saying it was an "exciting morning."
"What an exciting morning! The news makes me as happy this time as the very first time I was nominated. This nomination comes because Bill Hader and Alec Berg had faith in me since way back in 2016," Winkler said.
His costar, Hader, was also nominated for the outstanding actor in a comedy series for his role as Barry Berkman/Barry Block in Barry. "I'm just super happy and proud of everyone on the show and humbled and thrilled with the recognition and nominations," Hader said.
Anthony Carrigan was also nominated for outstanding supporting actor in a comedy series for playing NoHo Hank in Barry. "To be on such a special show like Barry is already the greatest gift, but this takes it to the next level," Carrigan said in a statement shared with PEOPLE. "It's an honor to be nominated alongside so many incredible actors. Feeling a lot of gratitude right now…"
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The 74th Primetime Emmy Awards are being broadcast live on NBC from the Microsoft Theater in Los Angeles.