Cahill and Holman sink Serbia but battling Socceroos are forced out on goal difference

Australia 2 Serbia 1

Australia bowed out of the World Cup last night despite their best performance of the tournament, which saw them beat Serbia. Second-half goals from Tim Cahill, a thunderous header in the 69th minute, and Brett Holman four minutes later with a fierce drive from outside the box, sealed Australia's first victory in Group D but Germany's win over Ghana elsewhere means the Australians will not progress to the last 16, as they did in 2006.

Serbia's goal came through Marko Pantelic six minutes from time. Serbia, who beat Germany 1-0 in their last match, lost their chances of advancing and finished bottom of the group.

"I'm just disappointed we don't go through. We have four points, I thought it might be enough," the Australia coach, Pim Verbeek, said. "In the end the goal difference against Germany killed us."

Despite the defeat, one Australian who would have taken some satisfaction from the evening is Tim Cahill. The Everton midfielder, sent off in the game against Germany, was clearly mortified to have landed his side in trouble in that game and he wheeled away in delight having given the Aussies the lead. "We've been through some hard times here," Cahill said.

It was a fine header but Holman's goal to double the Antipodeans' lead was, if anything, better. This World Cup has seen balls flying here, there and everywhere from distance but Holman hit it sweetly from more than 30 yards out and the ball bounced just once before it whistled into the net.

At that stage Australia would still have had thoughts of qualification for the next stage but Serbia's reply in the 84th minute ended those. Then it was the Europeans who could have gone through with an equaliser, but they were denied in the final minute when Nemanja Vidic headed the ball against the hand of an Australian defender – but the Uruguayan referee, Jorge Larrionda, waved play on.

Seconds later the World Cup dreams of both Australia and their Serbian rivals were at an end, but both can take some good memories home with them from South Africa.

Australia (4-5-1): Schwarzer, Wilkshire (Garcia, 82), Neill, Beauchamp, Chipperfield; Emerton, Culina, Cahill, Valeri (Holman, 65), Bresciano (Chipperfield, 66); Kennedy.

Serbia (4-4-2): Stojkovic; Ivanovic, Vidic, Lukovic, Kolarov; Krasic (Tosic, 62), Kuzmanovic (Lazovic, 77), Stankovic, Jovanovic; Zigic (Pantelic, 67), Lazovic.

Referee J Larrionda (Uruguay).

Man of the match Cahill.

Attendance 38,836.