England and America played out a 1-1 draw in Rustenburg on Saturday, with goalkeeper Robert Green the culprit of a disastrous blunder that gifted Dempsey an equaliser, after the Fulham man had hit a speculative shot from range.
"Honestly it seemed during the game that they were dealing with a lot of pressure," he said in The Sun.
"I don't know why that is, you could just sense it a little bit. Even though they did score early, when we came back and we equalised, they just seemed edgy. They really did.
"You would think these players would be full of confidence. There just seemed to be an edge to the team but it could have just been the opening game.
"You would have to ask them if it affected their performance. But they were edgy, there was an edginess to their game but I think they're a team with quality and they should play with confidence."
On Green's dreadful blunder, Dempsey added: "It's probably a save the keeper should have made. I didn't expect it to go in.
"When you hit it, you're kinda like 'Mmmm does it have a chance?' and then you see the keeper mishandle it and you're excited."