In his most animated comments following his side's last gasp 1-0 victory over Algeria which sent them through to the next round, Bradley said his players had been moved by their fans' strength of support.
"One of the nicest things tonight was when we were coming to the stadium, the street was lined with U.S. supporters, waving flags, dressed up, chanting USA and knocking on the bus," he said, with a slight smile on his face.
"We don't always have that. To have that in the World Cup in South Africa, I think I can speak on behalf of all the players, that was a really special feeling.
"And to finish tonight with a great win to go hand in hand with the kind of support we do have, it shows that we are making big steps."
Soccer is still a growing sport in the United States, having to compete with the more high profile basketball, baseball and American football, but viewing figures during the month-long tournament are almost double those who tuned in four years ago.
The U.S. soccer team's opening game against England drew almost 17 million viewers between English and Spanish-language channels, making it the country's most viewed first-round World Cup match ever.
The match on Wednesday was followed by thousands of U.S. fans in the stadium dressed in red, white and blue, who chanted throughout the match, making themselves heard over the din of the vuvuzela trumpets.
Landon Donovan, for years the pin-up boy of U.S. soccer, said the reaction from their fans would change forever the way he looked at the game.
"I used to see this game we played as just a game and I think I've realised, particularly at this tournament, that it's more than that," he said, after scoring the injury-time winner in a match watched by former President Bill Clinton.
"It's an opportunity to inspire, and not only inspire other people but inspire yourself. I think tonight is going to do a lot more for me and other people than maybe we realise."
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