There’s just one thing about Claire Danes that annoys Matthew Rhys.

Speaking to PEOPLE exclusively at Netflix’s FYSEE Fall Edit for The Beast in Me on Nov. 7, Rhys, 51, opened up about his relationship with costar Danes, 46. When asked what bugs him about his close friend, Rhys says, “The capacity she has for perfectionism is infuriating.”

“She is professional to the nth degree,” the actor adds.

In her response to the same question, Danes kept her answer simple, saying, “Really nothing. Truly. I’m not being diplomatic.”

“He really is just a lovely guy in addition to being a brilliant actor,” she continues. “There was no friction … We saved all of it for the television screen.”

Claire Danes as Aggie Wiggs and Matthew Rhys as Nile Jarvis on ‘The Beast in Me’.Courtesy of Netflix

Though the acclaimed actors play neighbors with a cat-and-mouse relationship in the new drama series, Danes and Rhys are good friends in real life. In their interview with Extra TV, Danes said working with Rhys on the show was “very pleasant.”

Rhys chimed in with, “I do think those pieces tend to kind of breed a greater sense of fun on set just cause you need to release the valve a bit after cut.”

Matthew Rhys as Nile Jarvis in ‘The Beast in Me’.Chris Saunders/Netflix

The Beast In Me details author Aggie Wiggs’ (Danes) investigation into her next-door neighbor, Nile Jarvis (Rhys). Nile was once the prime suspect in his wife’s disappearance, and Aggie is interested in making him the subject of her new book.

Along with Rhys and Danes, the series, created by Gabe Rotter, stars Brittany Snow, Natalie Morales, David Lyons and Tim Guinee.

In a November interview with PEOPLE, Rhys shared what he loved most about playing a “mildly sadistic” character.

“There’s a relish to Nile in that there’s a relish of the discomfort around him that he thoroughly enjoys,” Rhys said. “And I think sometimes he does that for his own entertainment, for his pleasure, for his mildly sadistic nature.”

He continued, “But then when he finds a kind of tennis partner in Aggie, and he goes, ‘Oh wow, this is someone who can hit the ball back at a far greater speed and far more deftly.’ So, that’s always fun.”

Rhys noted the connection between Aggie and Nile was unlike anything he had explored before in his previous work.

“It was certainly a relationship I’d never got to play before,” Rhys said. “And that was the kind of crack in the center of it for me, that when the real suspense is just in two people talking, then you’ve got gold.”

The Beast in Me is now streaming on Netflix.