Jones's first match in charge of his second stint coaching Australia was a horror show as his team were smashed 43-12 in front of a bumper crowd at Loftus Versfeld in Pretoria.
The Australian has only a few days to turn things around, with the Wallabies to meet Michael Cheika's Argentina in Sydney on Saturday.
Cooper, who emerged unscathed from his first match for the Wallabies since an Achilles injury nearly 12 months ago, said the loss was the first step in a journey to the World Cup under Jones.
"With every journey, it's never smooth sailing. Under Eddie's guidance, we will work towards that goal, which is to be World Cup champions," he told Australian media.
"Any loss is obviously a tough pill to swallow. There’s a hell of a lot of lessons in that game.
"As a team, we haven't had a lot of time together. It's continuing to build our combinations the way we want to play and build belief and clarity in that."
Rugby Australia appointed Jones to lift the Wallabies in a World Cup year after sacking former coach Dave Rennie in January.
However, Australian media detected little progress under Jones' stewardship and declared the new coach already under pressure.
"In the end, the Wallabies’ performance in Pretoria showed no real sign of progress from the Rennie years – particularly the discipline – and in several areas, the Australian side even regressed from the Spring Tour," rugby journalist Iain Payten wrote in the Sydney Morning Herald.
Jones lashed out at a South African reporter during the post-match media conference when questioned whether he was relieved the Wallabies had faced a South Africa "B" team, a reference to the slew of Proteas players rested from the game.
"South Africans are good at winning. You don't have to be a smartarse, mate," said Jones, who continued to berate the reporter after the press conference finished.
The widely reported outburst briefly shifted the spotlight from the players' performance.
However, there will be few places for the players to hide on Saturday when they meet the Pumas in front of home fans at Western Sydney Stadium.
