The west Africans drew the match 1-1 despite their opponents playing most of the game in Rustenburg with 10 men after Harry Kewell's early dismissal.
But Milovan Rajevac's team played with two teenagers at the heart of defence after first-choice centre-back pair of Mensah and Isaac Vorsah were ruled out through injury.
It meant that 19-year-olds Jonathan Mensah and Lee Addy came in to win their sixth and 12th caps respectively. Skipper John Mensah felt his side faired excellently under the circumstances, contrary to criticism dished out at the coach for not attacking more.
"We know people were expecting us to win, but many of our regular players were missing," he told Press Association Sport. "The two boys that stepped up did well.
"It was not a normal game. It was an international game and one at the World Cup. We must understand that and we should note that they delivered for the nation."
The draw put Ghana top of Group D with four points, one clear of Germany and Serbia, while the Australians have one point.
Mensah now believes that most of the pressure heading into the final game against the Germans will be on the three-time world champions, who must win to guarantee qualification.
"I don't think there is pressure now going in against Germany," he said. In fact they will probably have more pressure because they are favourites.
"We all know Germany has a good team, but we believe we have a good team as well. What we need to do against the Germans is be compact because when we play this way it brings us victory."
The 27-year-old, who spent the last season on loan at Sunderland where he struggled with back problems, did not want to disclose the nature of his latest injury.
Asked if he would be fit to face Germany, he said: "I hope so. My injury only came about at training (on Friday). It was really disappointing for me, but the doctors are keeping an eye on me and doing everything possible to make sure I am will be able to play the next game."