Tim Cahill scores Australia's opening goal
Australia manager Pim Verbeek was left to regret his side's opening 4-0 Group D defeat by Germany as the Socceroos exited the World Cup in South Africa.
Australia finished with four points following a 2-1 win over Serbia, but Ghana qualified in second place because of their superior goal difference.
"In the end the goal difference against Germany killed us," said Verbeek.
"We can't blame any of the players who did a great job and worked hard when everyone thought it was over."
Goals from Tim Cahill and second-half substitute Brett Holman scored for Australia in Nelspruit before Marko Pantelic's late goal set up a frenetic finish at the Mbombela Stadium.
An equaliser would have secured Serbia's place in the last 16 at the expense of Ghana, but substitute Pantelic wasted two good opportunities to level the score in the final minutes, much to the frustration of Serbia boss Radomir Antic.
Cahill, who returned to the Australian team after serving a one-match suspension for a red card in the defeat by Germany, lavished praised on his team's performance.
"A lot of respect for the lads. We've been through some hard times here," said the Everton midfielder.
"You see guys who will play their hearts out and run all day and then others come on and do the same thing. We have a team that works together and the team is fantastic."
He continued: "The way we played against Ghana and tonight, you can't ask for anything more. Four points in a competition like this is exceptional and we're very unlucky not to go through.
"I said during the week [that] if we won this game and got knocked out, we'd still be very proud Australians. We beat a great team that has got great results at this tournament."
Australia had the second-oldest squad in the tournament, with nine players aged 30 or over, including Cahill - but he vowed to continue his international career, irrespective of the decisions of others.
"I'm very proud to be part of this team and this nation. For me, I give everything. The only thing that'll stop me is a serious injury or something like that. I'll play for as long as I can," he said.
"It's a good thing if we can keep the core of boys that are in and around the squad but if some want to retire then I respect that because they have put their heart and soul on the line and you can't ask for more than that."