Aussies show grit to eliminate Serbia
Cahill put the Australians ahead with a glancing header from Luke Wilkshire's cross in the 69th minute and Holman added the second from long range four minutes later.
"A lot of respect for the lads. We've been through some hard times here," said Cahill, who was sent off in the team's opening match. "I'm just buzzing to hit the back of the net because this time last week my World Cup was over."
Marko Pantelic pulled a goal back for Serbia in the 84th, and then had a chance for a late equalizer but couldn't control a bouncing ball. If Serbia had drawn, the team would have advanced ahead of Ghana.
"I'm just disappointed we don't go through. We have four points, I thought it might be enough," Australia coach Pim Verbeek said. "In the end the goal difference against Germany killed us."
Australia's defense had been torn apart by Germany's wide players in its opening 4-0 loss and Serbia's early attacks were concentrated down the wings through Milos Krasic and Milan Jovanovic.
"We did our best, everything we could," Serbia coach Radomir Antic said. "This was a good game and I can't reproach my players as we had plenty of chances that we didn't take. In the end, we deserved more than what we got and now we have to go back home."
Serbia should have scored in the 12th minute when Milos Ninkovic broke through midfield from an Australia corner and put Krasic clear, but the winger was forced wide by goalkeeper Mark Schwarzer and shot off target.
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Schwarzer also did well to block defender Branislav Ivanovic's effort from close range, while Nikola Zigic should have done better with a free header from Zdravko Kuzmanovic's cross in the first half.
Krasic was jeered until his substitution in the 62nd as the majority Australian support in the crowd thought he had dived looking for a penalty in the second minute.
When the Socceroos did finally get the ball into a better crossing position, Mark Bresciano's delivery was skewed wide by Cahill rising at the back post.
"You see guys who will play their hearts out and run all day and then others come on and do the same thing," Cahill said. "We have a team that works together and the team is fantastic."
Australia started the second half brightly and Bresciano, Cahill and Jason Culina all tried their luck from distance.
"We wanted to continue in the second half with the tempo of the first but we are human and the missed opportunities depleted our morale," Antic said. "When Cahill jumped and scored, that was a shock for us and we lost our balance."
Serbia looked beaten, but Pantelic's late goal made for a frantic finale. An equalizer would have put the Serbs through, but Australia's defense held.
"It was a great result and great performance," Verbeek said. "But we are not in the final 16 and that was the plan when we came here to South Africa.
"We can't blame any of the players who did a great job and worked hard when everyone thought it was over.
Australia made the round of 16 four years ago but lost to eventual champion Italy.
"Four years ago four points was enough," Verbeek said. "This time it was not enough."
Australia: Mark Schwarzer; David Carney, Lucas Neill, Michael Beauchamp, Luke Wilkshire (Richard Garcia, 82) Mark Bresciano (Scott Chipperfield, 66), Carl Valeri (Brett Holman, 66), Jason Culina, Brett Emerton, Tim Cahill, Josh Kennedy.
Serbia: Vladimir Stojkovic; Ivan Obradovic, Nemanja Vidic, Aleksandar Lukovic, Branislav Ivanovic, Zdravko Kuzmanovic (Danko Lazovic, 77) Dejan Stankovic, Milan Jovanovic, Milos Ninkovic, Milos Krasic (Zoran Tosic, 62), Nikola Zigic (Marco Pantelic, 67).