Kevin Bacon: Sosie 'Blew Our Minds' at Golden Globes

01/13/2014 at 03:45 PM EST

Kevin Bacon: Sosie 'Blew Our Minds' at Golden Globes
Sosie and Kevin Bacon
Jason LaVeris/FilmMagic
Apparently star power runs in the Bacon blood.

Sunday night's Miss Golden Globe, Sosie Bacon, managed to impress even her A-list parents, as she pulled off her center stage duties effortlessly.

"I hadn't really imagined the amount of press and pressure and interviews and doing this kind of stuff that she would be asked to do," the 21-year-old's dad Kevin told PEOPLE on Monday at a Television Critics Association event in Pasadena, Calif., while promoting the second season of The Following. "She just handled it great. It was like she'd been doing it her whole life. It blew our minds. We were sort of like, 'Wow, how does she know how to do this?' "

Sosie's mom, Kyra Sedgwick had joked to PEOPLE she expected her daughter to "freak out and melt down," but that of course never happened.

"I thought she was great," Kevin added. "This year she made a decision that she really wanted to pursue acting full-time and all of a sudden got this opportunity to be Miss Golden Globe."

It's not that Sosie's parents didn't believe in their little girl. They just never really exposed her much to celebrity events and the kind of work they do.

"We have kept our kids pretty much out of the spotlight," Kevin explains. "We did for many, many years. Up until the time they were about 15, I don't think you could even find a photograph of them unless it was snapped on a beach somewhere. We just didn't take them to events and we just kind of kept that part of our lives separate."

Up next for the fresh face?

"Well, hopefully a job," Kevin said with a laugh. "You know, she's auditioning a lot. She has very good agents and very good management and she's got two small films that she did that are coming out. She's out there playing the game like the rest of us."

Related Video: Meet Kevin Bacon's New (Extended) Family Band

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