The goalkeeper made 15 saves in the match, which is more in a single game than any other player in World Cup history.
"Tim Howard played phenomenal," BBC Sport quotes Klinsmann as saying. "He was outstanding and he kept us in the game.
"We knew we would have chances if we kept going forward but he was absolutely amazing. You can give him the biggest compliments in the world. The longer he keeps you in the game you hope that you will get the breaks going forward.
"You can build on the back of Tim. Games are decided by little things and thanks to Tim we had that possibility throughout 120 minutes."
Howard, who has been an ever-present during the USA's World Cup campaign, was making his 104th appearance for the national side.