Grim-faced American players filed by one by one on their way out of Royal Bafokeng Stadium. Their World Cup was over. They'll have four long...

RUSTENBURG, South Africa — Grim-faced American players filed by one by one on their way out of Royal Bafokeng Stadium. Their World Cup was over.

They’ll have four long years to dwell on what might have been, how the most-talented team in U.S. soccer history was knocked out in a game the Americans were convinced they should have won.

No nail-biting comeback this time. The U.S. relied on late rallies once too often.

Life on the World Cup edge came to an exhausting and crushing end against a familiar foe Saturday night, when Ghana — led by Asamoah Gyan’s goal three minutes into overtime — posted a 2-1 victory that ended a thrilling yet futile tournament for the United States in the second round just when it seemed the Americans had a relatively easy path to the semifinals.

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“We felt like we had a great opportunity,” goalkeeper Tim Howard said. “We just gave ourselves too much of a mountain to climb. We just couldn’t come back.”

Kevin-Prince Boateng put Ghana ahead when he stripped the ball from Ricardo Clark in the fifth minute and beat Howard from 16 yards. It was the third time in four games the U.S. fell behind early, and once again the Americans rallied.

Landon Donovan tied the score with a penalty kick in the 62nd minute, his record fifth goal for the U.S. in World Cup play, after Jonathan Mensah pulled down Clint Dempsey streaking in. But that was it.

There was no offense left, no spark, no fire — unlike the first-round come-from-behind draws against England and Slovenia, and Donovan’s memorable injury-time goal against Algeria that lifted the U.S. into the knockout phase.

“We tried to push and push,” U.S. captain Carlos Bocanegra said. “I don’t know if we just didn’t have anything left because we had been pushing so much the entire tournament.”

Ghana, the only African team to advance past the first round of Africa’s first World Cup, eliminated the Americans for the second straight World Cup after a 2-1 win that knocked out the U.S. in the group phase in Germany. The Black Stars joined Cameroon (1990) and Senegal (2002) as the only African teams to reach the quarterfinals and will play Uruguay for a berth in the semifinals, a round the U.S. has not reached since the first World Cup in 1930.

“A stinging, tough defeat,” said Bob Bradley, who faces an uncertain future as U.S. coach.

With former President Clinton watching and Mick Jagger sitting next to him, the U.S. was done in by a porous defense and forwards who failed to score a goal in four games.

“When you give up this many goals, you’re not going to go very far,” Bocanegra said.

All five U.S. goals in the tournament came from the team’s midfield backbone: three by Donovan, one by Dempsey and one by Michael Bradley, the coach’s son.

In the first overtime World Cup game for the U.S., Gyan got the winning goal when he took a long ball from Andre Ayew over the defense and beat Bocanegra, his teammate on the French club Rennes. Gyan let the ball bounce, took a touch with his chest, and with Jay DeMerit vainly trying to catch up, scored over Howard with a left-footed shot from 16 yards.

“I had my angles right there. There no question about it,” Howard said. “He absolutely crushed it.”