The actor said he had fun with Efron, 36, on set by referencing his breakout role in the High School Musical franchise.
"I sung [some of 'Breaking Free'] to Zac when I was playing my music scene. That was definitely a life experience that I'll never forget," Simons said when asked about working with someone he grew up watching.
"When I was singing the song, he was like, 'Oh, you're not hitting it, you're not hitting it.' I was like, 'Oh,' and I redid it. And I think I did a good job!" he added.
Simons didn't stop there. "When we were in the ring I was like, 'I got to get my head in the game,' " he continued, name-checking another song from the first film, released in 2006.
The actor says he "just had to not think about" the fact that he was working alongside such a seasoned star he was familiar with ahead of time.
"And Lily James was Cinderella! I had Troy Bolton and Cinderella in one scene together," he added, joking, "It was a little bit of a mind— I don't want to say the word."
Simons plays the youngest of the Von Erich brothers depicted in The Iron Claw, Mike, alongside Efron as Kevin plus Jeremy Allen White as Kerry and Harris Dickinson as David.
"We really bonded and got to hang out," Simons said of their time making the film. "When we got on set it just felt natural. They were really welcoming to me, not just my brothers but all the cast members. So it was a little nerve-racking, but they just were very open."
Kevin is the only surviving Von Erich brother (a group that also includes Chris Von Erich, not depicted in the film).
The retired professional wrestler, now 66, appeared at the premiere alongside the cast, where he told that Efron "had a tough job" in stepping into his shoes.
"It's not easy to be me. I wrestled seven years World Class, but then I wrestled 22 years," Kevin said. "That's a whole lot to cram into a movie, but he was able to do it ... he's a real star. They all are."
Asked whether he has seen High School Musical, Kevin said, "I didn't see that one, but I'm sure [Zac] did well."
The Iron Claw is in theaters Dec. 22.