Highlights: USA 1-2 Ghana (aet)
United States coach Bob Bradley said he and his players are proud of their achievements despite their elimination in the last 16 at the hands of Ghana.
Asamoah Gyan's extra-time strike gave Ghana a 2-1 victory over the US in a hard-fought contest in Rustenburg.
"We're disappointed we couldn't take it further but this is a terrific group and we're proud," said Bradley.
"We knew Ghana was a good team and we didn't get the job done. It is a stinging, tough defeat."
Gyan's powerful strike for Ghana, three minutes into extra-time, proved decisive in the game.
The US had the better of the second half in Rustenburg, having deservedly drawn level when Landon Donovan's penalty cancelled out Kevin Prince Boateng's early opener for the Black Stars.
Donovan levels for USA from the spot
"I really felt when we got to 1-1 there were some chances for us," said Bradley.
"Early in the overtime we go down again early. At that point, with everything we put into the game early, we didn't have enough after that."
The US had relied on late goals to earn their progression to the second round.
In the group stage, Michael Bradley's late strike earned them a 2-2 draw with Slovenia and Donovan's injury-time winner against Algeria ensured they topped Group C and lined up the last-16 tie with Ghana.
But the US were unable to replicate such heroics against Ghana, who will now go on to face Uruguay in a quarter-final clash in Johannesburg on Friday.
Donovan's penalty - awarded after Clint Dempsey was fouled by Jonathan Mensah - was the striker's third goal of the tournament and his fifth World Cup goal in total, making him his country's leading all-time scorer in the competition.
"We were a little naive tonight and at this level you can't do that," said Donovan. "It is frustrating considering all the work we have put in, it just sucks man.
"I'm proud of what the team has done. Soccer is a cruel game sometimes. One minute you are on top of the world, the next minute you are at the bottom of the mountain."
Gyan blasts Ghana into extra-time lead