Australia's 28-8 capitulation to the Springboks in Cape Town on Saturday was their fourth loss from five matches in the Rugby Championship.
A loss to Argentina in Rosario this weekend in the final round would likely see the Wallabies finish bottom of the southern hemisphere competition, and heap further pressure on new coach Ewen McKenzie.
McKenzie, who replaced the deposed Robbie Deans after the lost British and Irish Lions series, has been criticised for tweaking his selections throughout the tournament with little success, but Cooper said the fault lay with the players.
"There's a way that Ewen is coaching the team, everybody's got to buy into that and adapt to it as well," Cooper told Australian media in Cape Town.
"We can't keep using excuses, we've run out of excuses as a team in terms of how we go about each week.
"We've just got to put it down to hard work, sticking together as a team, backing our coach, backing our players, and we've got to strive for more success. We're not going to shy away from the hard work that's in and amongst us."
Australia's run of abysmal form has sparked derision on social media and put the country's sceptical rugby media up in arms.
Local pundit Greg Growden described them as "one of the worst Wallabies teams in 30 years" in his column on ESPNscrum.
"It has been some time since the Wallabies have appeared in a Test match with so many players who are realistically struggling to convince anyone but themselves that they are of international standard," Growden fumed.
Australia cobbled a scratchy one-point win over Argentina in their clash in Perth, but few commentators Down Under feel optimistic about another win in Rosario, especially after the Puma forwards' impressive performance against the All Blacks in La Plata.
Australia's struggles at set pieces have reached alarming levels in the Rugby Championship and Argentina's forwards will be keen to exploit their opponents' weakness in front of home fans.
Cooper warned that there might be further pain in store for Wallabies fans as the team works to rebuild confidence.
"We'll get there. It's all in due time but I urge everyone, it's not going to happen overnight," he said.
"It's something that we've got to continue to be upbeat about but we've got to know that it's a tough process and it's something that will come, but right now it's just not happening."