Clinton was sitting in the stands with dignitaries at Loftus Versfeld in Pretoria on Wednesday when forward Landon Donovan got a winner in added time to send the U.S. into the last 16.
"I lost my voice yesterday. I was very diplomatic until we scored," Clinton said in an interview with a roundtable of journalists on Thursday.
"When that sucker went in there, I said, 'Thank God for overtime'," he added, having joined in the celebrations after a pulsating 1-0 win over Algeria on Wednesday that left the U.S. top of Group C above favourites England.
"Both the United States and Algeria played that game with both their minds and their hearts in the right place."
Clinton went to the U.S. changing room after the match, where he said some players asked him to stay for a beer, or two.
"In the locker room, all they talked about was how they played as a team. They were a happy crowd yesterday."
GRUDGING RESPECT
Clinton, who was introduced to football when he went to England as a Rhodes Scholar in the late 1960s, has been impressed with the way the U.S. squad has overcome adversity, including having two goals disallowed.
He plans to attend the next U.S. match against Ghana in the second round in Rustenburg on Saturday.
The former U.S. leader said while the world's football powers do not see the United States as reaching their level, there is a grudging respect for the battling Americans.
"Argentina and Brazil think that we are better at this then we are," he said. "Others have been doing it longer. That is OK. I think they believe that we are serious about it now."
Clinton, president when the U.S. hosted the World Cup in 1994, has been in South Africa campaigning to bring the event back to the States, where he said every team can find a home base of support among the various ethnic groups in the country.
"It would be really good for America if we could do it. I think it would be good for soccer worldwide if we could do it."
Clinton has also pondered how the sport can be used as a proxy for peacefully battling over the ethnic and political issues that have persistently divided countries and peoples.
"The real trick is not to ask people to give up the particularities of their identities but to give them a place to put it that is not destructive," he said.
