The Barcelona playmaker was allowed little room to manoeuvre by a tigerish American side who reached their first major final.
"We made a special point to close down Xavi, trying to force him to play the ball square or behind him so that he couldn't play any of those penetrating passes he is so good at," Bradley told reporters.
"We did a very good job of sealing down the middle of the field. When you play Spain you have to work hard as a group to defend and when we had the ball we needed to be aggressive."
Bradley paid special tribute to central defenders Jay DeMerit and Oguchi Onyewu, who thwarted a furious Spanish onslaught in the second half.
"To go from the first two games and concede six goals to the next two games and not concede any is a tremendous effort from everybody on the team," said Onyewu.
Goalkeeper Tim Howard added: "We are scratching our heads just like you guys are but it goes to show what hard work and commitment to each other can bring. Football is a funny thing.
"Any time you come away with a shock win you need to take your chances in front of goal and we defended like bandits. We rode our luck today."
Goals from Jozy Altidore and Clint Dempsey sank the world's top-ranked team. It ended Spain's world record run of 15 successive victories and their 35-match unbeaten sequence, a world record streak they share with Brazil.
The U.S. now meet holders Brazil or hosts South Africa in Sunday's final.
