On Olympic debut, 19-year-old Jakara Anthony was exceptional as she claimed fourth after scoring 75.38 in the Super Final.
Cox headed into the Super Final with the second highest score in Final 2 before scoring 75.08 to claim fifth place.
Perrine Laffont of France won the gold medal with a score of 78.65, with defending Olympic Champion Justine Dufour-Lapointe of Canada claiming silver and Kazakhstan's Yulia Galysheva taking the bronze medal.
“I had a lot of runs today and they progressively got better," said Anthony.
"I think my first two final runs were my best and then full on day so by the time you get to the Super Final it starts to drop off a bit. It wasn’t my best run of the day but I’m still really happy with how I performed.
“The whole thing’s been a massive learning experience for me and I’ll definitely be taking all the experience that I had here going into Beijing 2022."
After having to come through qualification 2 to make the top 20, Anthony produced one of her best runs of the competition with a score of 76.81 to move through to the final 12 in fourth place. She then finished the second final in 4th with a score of 76.85.
Cox closely followed Anthony with a score of 75.79 to make the top 12 in 5th before then scoring 78.28 to move into the Super Final in 2nd.
“My goal for this week and for tonight in particular was to absolutely go for it, give it everything I’ve got and I really truly believe that I did that tonight so for that I’m really happy and I’m really proud," Cox said.
"It didn’t really pay off for me in the Super Final, I went too big and too fast and was scrappy in the middle but I achieved my goal of going for it so that’s a positive and I’m proud of that”
Over the past eight years Cox has seen the sport develop sport so much in Australia and she is not only proud of her perforance but also that of her teammates.
“This is my third Games so it’s not my first rodeo but I’ve thoroughly enjoyed this experience.
"I've especially enjoyed being part of a full team, it’s been so exciting with this being the first time we’ve ever had four women from Australia competing in the moguls so I’m really proud to have three other teammates there skiing alongside me.
"That’s super exciting but I’m definitely looking forward to the next four years and to Beijing in the future.”
Madii Himbury, who had earlier progressed from qualification 2 scored 68.19 to finish 20th overall.
Himbury said it was “pretty exciting” to make it into the finals.
“I squeezed into the top 20, just, and I was hoping to go a bit faster and a bit bigger and I did," she said.
"I just had a little mistake on the bottom there, drifted a little and so didn’t get the score that I’m hoping for but I did what I wanted to do and I went for it so I’m happy.
“It’s been pretty good, the noise carries as well so we can hear all the cheers up in the start gate. We’ve got lots of friends and family here so it was all very exciting.
Claudia Gueli unfortunately had a fall between her two jumps in qualification 2 and finished 23rd overall.
"That was really fun, I was happy with my skiing up until the little hiccup, but regardless it’s been such a journey so I can’t complain," said Gueli.
"It’s pretty good conditions, the course is a bit firmer because it’s colder today but we’re used to it from other courses around the globe.
"I got an edge, I was a bit too over the wrong foot on one of the turns and once that happens it’s really hard to come back from so I pulled out, tried to save myself but it doesn’t always pan out the way you want it to.
"I'm going to go home and rest up and start training in about a month to prepare for the next year."