Flight Attendants Association of Australia spokesperson Teri O'Toole said the issue had created a tense situation between the union and Qantas over working conditions, according to Daily Mail Australia.
"The crew have tried to get some privacy by making a fort like little kids out of blankets to give themselves privacy, which is just a disgrace," she said.
"It's not appropriate rest in the workplace. It's not appropriate rest for anyone."
She claimed that while the union pushed for an extra day of rest for employees to compensate for a lack of sleeping facilities on A330 planes, Qantas had instead switched from Australian to New Zealand crews, leaving many Australians without work.
The airline has been accused of using its UK and New Zealand-based crew on international flights instead of its Australian workforce, leaving many local workers on extended reserve rosters, in order to save cash.
However, Qantas has denied that it is outsourcing jobs, or that any of these decisions were made based on cost.
Qantas cabin crew executive manager Rachel Yangoyan said the airline was working on a long-term solution that would create a private area for flight attendants to rest.
"A small amount of flying is being done by New Zealand-based crew because the union was not prepared to support Australian-based crew working on longer routes with some of our A330 aircraft, including the Brisbane to Los Angeles route, on terms that we were able to agree to," Yangoyan told Australian Aviation.
"We wanted to have our Australian-based crew do this flying, but without the union's support for this to happen, we've instead had to use New Zealand-based crew on some of these flights."
According to the publication, official crew rest areas on the Airbus A330 are generally set aside for the four pilots onboard, while cabin crew are often assigned designated areas in the passenger cabin to take their breaks. Aviation fatigue management rules dictate that A330 crew are required to have a lie-flat option during their rest time onboard.
"It's really important to note that what you've seen currently is actually not what the long term solution will be," Yangoyan said.
"What they will have installed in around six weeks is a full curtain that wraps around that lie-flat rest area.
"But in the interim, while we've been operating without that curtain, we have changed the timing of those flights so that they are operating during the day [and] our crew don't need as much sleep time as they would typically need if we were to operate these flights during the evening.
"We've also looked at some additional rest that we're giving these crew in Los Angeles and also when they return home.
"'Once we get that curtain in place, we're really confident that this will be a private area with a lie-flat bed, where our crew really will be able to get some adequate rest on these longer duties."