United States boss Jurgen Klinsmann paid tribute to Tim Howard's "phenomenal" performance as the Everton goalkeeper defied Belgium until extra time.
Howard made 16 saves, the most by any keeper in a World Cup match since 1966 according to statistics, before two goals in extra time saw Belgium win 2-1 to secure a quarter-final place against Argentina.
Klinsmann said: "What Tim played tonight was just phenomenal, outstanding - he kept us in that game for a long time. We are proud to have him with us.
"It was an absolutely amazing match tonight and you can give him the biggest compliment in the world."
The introduction of Romelu Lukaku - Howard's Everton team-mate last season - made the difference, with the striker creating the opening for Kevin de Bruyne's winner before scoring the second himself.
Teenager Julian Green gave the Americans hope and they had chances, but Belgium just held out.
Klinsmann said it was "a bummer" for his side to lose, but insisted his players should be proud of themselves.
He added: "It's a bummer for us ending on the losing side after a game of 120 minutes that gave everything to the fans, a real drama, a thriller.
"We we had enough possession to equalise that game at the end, but a big compliment to Belgium and congratulations to them.
"I'm very proud of our team. Every player on the field made their country proud with this performance in this World Cup.
"All of the players just went beyond their capabilities and I told them they should take a lot of very positive stuff back home with them."
Belgium coach Marc Wilmots admitted it had been "scary" after Green's goal.
He said: "We had a lot of opportunities, and we dominated the game, and in the end it was well deserved even if it was scary with the US goal.
"Lukaku had been much criticised, and I told him, 'do not worry - the second round might be your day', and that's what happened.
"Tom Howard had a fantastic match but we need to forget about this match and focus on Argentina.
"There shouldn't be any more worries from the media about us not playing football."
Lukaku himself was modest about his impact, saying: "I'm not the hero - it's the team that is. There are many players who have made a big difference since the start of this competition."