Maggie Gyllenhaal tells PEOPLE that husband Peter Sarsgaard was "holding up the family side of things" while she made her award-winning directorial debut
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Maggie Gyllenhaal and Peter Saarsgard
Credit: Dimitrios Kambouris/Getty

Maggie Gyllenhaal is shining a light on husband Peter Sarsgaard's support while she took on a new challenge.

The actress, 44, directed the Netflix thriller The Lost Daughter, which stars Olivia Colman, Dakota Johnson, Jessie Buckley, Paul Mescal and Sarsgaard, 50, whom Gyllenhaal wed in 2009.

At the 31st Annual Gotham Awards, held at Cipriani Wall Street in New York City on Monday night, the movie won best feature, outstanding lead performance for Colman, plus two accolades for Gyllenhaal: best screenplay and the Bingham Ray Breakthrough Director award, which is given to a director for their first feature film.

Gyllenhaal told PEOPLE at the Gotham Awards that Sarsgaard's support was instrumental in directing the film.

"I really have respect for him," she says of the actor, with whom she shares daughters Ramona, 15, and Gloria Ray, 9.

"It's such a pleasure to direct him. He's in my film; he's hugely impactful in my film. But mostly, he was holding up the family side of things, and that is invaluable," adds Gyllenhaal. "I could not have made this film without that. There are so many examples of women gracefully, intelligently supporting their husbands and there are so few examples of men doing that for their wives. He's a really incredible example of that."

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Explaining how he took over parenting duties, Gyllenhaal shares, "You know, like making a doctor's appointment, making sure the girls had the right sized shoes. That's the kind of thing I do. But to know that someone else is picking up the slack, to let your mind have the space to do your work is a gift that without which I could not have made this film."

The Lost Daughter, an adaptation of Elena Ferrante's novel of the same name, stars Colman as a literature professor and mother of two grown daughters who goes on an extended vacation in Greece. While there, she encounters a vacationing family and a young mother who reminds her of her own dark experiences with parenthood.

"The film is about a lot of things, but one of the things that this film is about is how complicated it is to be a mother, so I don't think I could have really have explored those things and all of the complications without knowing that my family was taken care of," Gyllenhaal explains.

The Lost Daughter is in select theaters Dec. 17 and available to stream on Netflix starting Dec. 31.