The USA fell agonisingly short of reaching the FIFA World Cup quarter-finals for the first time since 2002 after extra-time goals from Kevin De Bruyne and Romelu Lukaku guided Belgium to a 2-1 win in Salvador.
American substitute Julian Green ensured a nervy finish with a 113th-minute goal.
Despite coming close to a last-eight clash against Argentina, Belgium threatened to run away with the match, if not for the heroics of Howard.
The 35-year-old thwarted Marc Wilmots' men on numerous occasions, making 15 saves - a World Cup record that surpassed the 13 set by Peruvian goalkeeper Ramon Quiroga in 1978.
"I have to say that what Tim Howard did tonight was phenomenal, outstanding and amazing," Klinsmann said afterwards.
"He kept us in the game. He had an absolutely amazing match and you have to give him all the plaudits. That said had chances to equalise, but congratulations to Belgium."
While Howard was busy in defence, the USA had chances of their own at the other end, none better than Chris Wondolowski in second-half stoppage time.
Wondolowski - a 72nd minute substitute - found himself unmarked on the edge of the six-yard box after Jermaine Jones' knock down but he fired his effort over the crossbar.
Despite the disappointment of losing in extra-time, Klinsmann could not falter the efforts of his players and said American football was on the right track.
"It's hard for us to end up on the losing side after 120 minutes of giving absolutely everything," he said. "But this game had everything, it was a thriller.
"I'm proud of the players not just for what they've done tonight, but what they've done throughout the tournament. They've made the country proud.
"The sport in the USA will only continue to grow. It's getting stronger and there's a lot to build on going forward."
