The slopestyle course is laid up in two parts with three rails features at the top and three large jumps at the bottom. Skiers are judged on difficulty of the run, execution of tricks, amplitude over the jumps and combinations of tricks and manoeuvres.
Willcox scored a tidy 62.40 on her first run and was sitting 12th but had difficulty on her second run and lost too much speed to tackle the last two jumps _ only the top score counts. She then watched as others pushed her out of a place in the final.
Willcox had decided to be more aggressive on the second run in the hope of qualifying for the final.
"As a developing athlete new to the Olympics, Anna certainly stood up and it was exciting to see,'' Winter performance programme director Ashley Light said. "She achieved what she set out to do, landed her run and achieved a credible result.
"Now that Anna knows that she belongs at this level, in the top 16, she can look forward to PyeongChang in 2018 where she can build on this result.''
The event was won by Canadian Dara Howell, who scored an impressive 94.20 in the final. It was also notable for the heavy crash by fellow Canadian Yuki Tsubota who is thought to have fractured her jaw.
Jossi Wells, who is considered New Zealand's best hope for a medal in Sochi, will compete in the men's slopestyle skiing qualifiers tomorrow tonight (NZT)