Vice-captain Josh Hazlewood believes the narrow win on Friday night has released some of the pressure that has been building for months after series defeats in England and the Middle East across all three formats.
While it is only two games into an international summer that does not finish until February, Stoinis, whose vigorous celebration of a wicket caught the eye of social media, said the players are already feeling the effects of all the controversy.
Stoinis said Australia's woes with the bat could be attributed to the "noise" that followed the release of the Ethics Centre's scathing review into the sport.
"People are drained. We're cooked right now and we just won. Maybe that's part of it, the mental drain, that's what we've got to work on, that's what we've got to get past," Stoinis said.
"The season goes all year, every year, backs up to last year, haven't stopped, so it's been a long time.
"You've got to learn, that's part of the art of playing international cricket is dealing with noise."
As happy as the Australian camp has been with the way they have trained, winning provides validation. The win was just Australia's third in the 50-over format from their past 20 completed games, and ended a seven-game losing streak.
"It’s a good feeling to have a win but at the end of the day it’s only one. With how much there’s been going on in cricket it’s a good start just to get a win," Stoinis said.
"I’m bloody tired. We’re all bloody tired. All the bowlers are cooked. It was a big effort. So really proud of everyone."
Hazlewood said Stoinis's comments were more relevant to those who took part in the tour of the UAE. Thankfully for Australia, whose fortunes this summer ride heavily on their attack, Hazlewood and Pat Cummins did not tour while Mitchell Starc missed the Twenty20s but stayed in the Middle East.