Joseph Gordons-Levitt reveals his wife squealed when he surprise-serenaded her with Taylor Swift ‘lover’

“She was shocked,” says the ‘Beverly Hills Cop: Axel F’ star, who spoke to PEOPLE for One Last Thing. “In the best way”

Joseph Gordon-Levitt knew he needed to get creative when he realized he would be out of town for his wife’s birthday.

The actor, 43, who lives in L.A. with his wife, Tasha McCauley, and their two sons, was doing press for his new Netflix movie, Beverly Hills Cop: Axel F, and was scheduled to appear on The Tonight Show Starring Jimmy Fallon on June 19.

“I felt absolutely terrible and knew I needed to do something,” Gordon-Levitt tells PEOPLE for One Last Thing in this week’s issue. “And the night that I went to do Jimmy’s show was her actual birthday.”

Knowing McCauley is a super-Swiftie when it comes to Taylor Swift, Gordon-Levitt proposed surprising his wife by serenading her on the show with his rendition of the singer’s hit song “Lover.”

“I think she would be embarrassed for me to say how big a fan of Taylor she is,” he says, laughing. “We went to the Eras Tour together. She’s been a fan long before it was cool to be a Taylor Swift fan.”

The first step was securing the rights to use the song on the show and the rest was set in motion. “We didn’t know if we would get the rights because it’s very difficult so I had to also pick a backup and that was very difficult,” the actor explains.

“I actually gained even more admiration for Ms. Swift as a songwriter as I was trying to find something else that would simultaneously be meaningful to my wife and meaningful to the wider world. It’s a really hard balance to strike. She’s a master, she’s truly awesome.”

Given the greenlight, Gordon-Levitt practiced a few times and then went for it during his appearance. As for his wife’s response? “Oh, she was shocked, yeah. In the best way,” he adds. “She sunk down into the couch squealing, I think.”