Skiing in her first World Championships, Cox finished in 17th while 22-year-old Hall improved on his only other World Championship appearance by placing 20th in the men's event.
Olympic Winter Games silver medalist and runner-up from the last World Championships Jennifer Heil from Canada won the gold,
Vancouver Olympic champion Hannah Kearney from the United States was second and Canadian Kristi Richards was third.
Frenchman Guilbaut Colas won the men's championship with Canadian duo Alexandre Bilodeau and Mikael Kingsbury filling the other two podium places.
Both Australians will be satisfied that their performances today were their best single moguls result recorded at either Olympic or World Championship levels and both gained valuable experience for their promising careers.
By finishing 17th, Cox missed qualifying for the final by just one place, which is eight places higher than her 23rd at the Vancouver Winter Olympics 12 months ago.
In other mogul results, Australians David Graham finished 24th and Nicole Parks crashed off the bottom air and was unable to complete the course.
The World Championships, being held at Deer Valley and the Park City Mountain resort in Utah, have attracted 36 nations and 313 athletes, significantly more than the previous event in Japan in 2009.
The mogul athletes will compete again in Saturday's dual moguls.