Turist, which was written and directed by Ruben Östlund, has already won other global awards including the prestigious jury prize at the Cannes Film Festival and had been widely tipped to win a Golden Globe award.
The plot revolves around a Swedish family on holiday in the French Alps and how they deal with the very near disaster of an avalanche.
But despite glowing reviews in the US, it missed out in the Best Foreign Film category at the ceremony in Hollywood on Sunday, to Russian film Leviathan.
Leviathan, which is directed by Andrei Zvyagintsev, is a drama about corruption in contemporary Russia.
"I'm not disappointed right now," Östland told Swedish news network SVT on Sunday.
"I think it's cool Leviathan won. The movie is great, Andrey Zvyagintsev is a talented director and the actors have done a great job."
Östland is now set to travel around the US promoting his movies.
"My films are going to 15 cities. I'm going to go to Washington, New York and Minneapolis to talk about my movies," he said.
Elsewhere, US director Richard Linklater's Boyhood was the big winner at the festival. The movie, which took more than a decade to film, depicts a boy in Texas growing up and won awards for Best Film, Best Director and Best Supporting Actress.
Last week, Turist got ten nominations at Sweden's version of the Oscars, the Guldbagge awards.
Director Ruben Östlund will find out on Thursday if it has made the shortlist for the 2015 Oscars.