The Americans showed an admirable fighting quality in staging several dramatic comebacks to force their way through to the knockout stages but their coach said giving away an early goal in the second round match at Rustenburg took a heavy toll.
"The fact we gave away a goal so quickly, it was going to be hard to get back," he said of the fifth minute strike by Ghana's Kevin-Prince Boateng that had the Americans on the back foot at the Royal Bafokeng Stadium.
"We put a lot into it trying to get back to 1-1. We put ourselves in that spot one too many times, expending too much energy."
The United States overcame the early deficit to take charge in the second half and equalise through Landon Donovan, who converted a 62nd minute penalty.
But Bradley said when they were caught again by a goal from Asamoah Gyan three minutes into extra time, there was nothing left in reserve to stage another fightback.
The United States came from behind against England to draw 1-1 their first game at the tournament in South Africa, then fought back from a 2-0 deficit to draw 2-2 with Slovenia.
On Wednesday, they were headed out of the tournament before a stoppage time winner from Donovan earned them top place in their group with a 1-0 win over Algeria.
"We felt we had the ability to go further. My initial feeling is disappointment that we didn't get past this game and continue to test ourselves," he said at a post-match news conference.
