The Stars and Stripes were knocked out of the tournament after being beaten 2-1 in extra time at the Arena Fonte Nova in Salvador.
Although Klinsmann's side came close to levelling the scores in the dying minutes of the match, the German is proud of what they had achieved during their time in Brazil.
"Obviously it's a bummer for us to end on the losing side in a game that gave everything to the fans and to the crowd. A thriller, we had enough possibilities to equalise in that game," BBC Sport quotes him as saying.
"Congratulations to Belgium. It was a game which went to the extreme. We are all very proud of our team, they gave everything they had and they made their country proud.
"The sport will only continue to grow. The league is getting stronger and stronger and we are into another four-year cycle of Olympics, Gold Cup, Copa America and World Cup."
Having beaten the USA, Belgium will now face Argentina in the quarter-finals at the Estadio Nacional on Saturday.