After a solid preparation, Cox was hopeful of a strong result to start the season, but the 18-year-old made an uncharacteristic mistake on a turn in qualifying which put an end to her hopes of making the dual finals.
However, she can take some solace with the knowledge that her speed down the 212-metre Ruka course appeared to have quickened since last season.
American Heather McPhie won the first mogul gold medal of the season ahead of Canadian Justine Dufour-Lapointe and Japan's Aiko Uemura.
Cox's AIS/NSWIS team-mate Nicole Parks was unable to compete in the event after tearing a ligament in her thumb during training which required surgery. Parks will resume competition in the North American World Cup's in January.
In the men's draw, AIS/NSWIS skier Matt Graham put down a top to bottom run, but went unrewarded from the judges to finish in 27th place.
Competing in his first full time World Cup season, Graham missed the round of 16 and had to be content watching Canadian Mikael Kingsbury stretch his run of podium finishes to 16 and claim first place
2010 Olympic champion Alexandre Bilodeau of Canada was second, with American Jeremy Cota in third.
"The standard of the field in year three of the Olympic cycle has improved significantly", AIS mogul skiing head coach Steve Desovich commented after the event.
"Both athletes are still quite inexperienced and we hope to improve over the course of the season"
The team now heads to the final World Cup of the calendar year in Kreichberg, Austria, which will take place on December 22.