SALVADOR, Brazil — They captured the hearts of America — from coast to coast, big towns and small, all the way to the White House.

Capturing the World Cup will have to wait.

Just like four years ago, the United States is going home after the round of 16, beaten when Belgium scored twice in extra time Tuesday and then held on for a 2-1 win.

“Thirty-one teams get their heart broken,” goalkeeper Tim Howard said. “It has to end sometime. It ended a little bit early for us.”

Playing the finest game of his career, Howard stopped a dozen shots to keep the Americans even through regulation and force an additional 30 minutes. He wound up with 16 saves — the most in the World Cup since FIFA started keeping track in 2002.

Before exiting, the U.S. showed the spunk that won America’s attention. The Belgians built a two-goal lead when Kevin De Bruyne scored in the 93rd minute and Romelu Lukaku in the 105th.

But then Julian Green, at 19 the third-youngest player in the tournament, stuck out his right foot to volley in Michael Bradley’s pass over the defense in the 107th, two minutes after entering.

“I was sure that we would make the second goal and we would go to the penalty shootout,” Green said.

The Americans nearly did. In the 114th, Clint Dempsey peeled away on a 30-yard free kick by Bradley, who passed ahead to Chris Wondolowski. He fed Dempsey, and goalkeeper Thibaut Courtois bolted off his line to block the 6-yard shot.

At the final whistle, the U.S. players fell to the field in their all-white uniforms like so many crumpled tissues.

“They made their country proud with this performance and also with their entire performance in this World Cup,” said Jurgen Klinsmann, the former German World Cup champion who took over as coach three years ago.

The Americans advanced from a difficult first-round group to reach the knockout rounds of consecutive World Cups for the first time. Four years ago, they were eliminated by Ghana 2-1 on a goal in the third minute of extra time.

“Getting to the round of 16, if we don’t do that, we’re very, very disappointed,” U.S. Soccer Federation President Sunil Gulati said. “We get here and it’s kind of the swing game. We get beyond here, then it’s generally viewed as very successful — this year was a little different because of the group we had in the first round, so that I think is already a success.”

The crowd of 51,227 at Arena Fonte Nova appeared to be about one third pro-U.S., with 10 percent backing the Belgians and the rest neutral. Back home, millions watched in offices, homes and public gatherings that included a huge crowd at Chicago’s Soldier Field.

President Barack Obama joined about 200 staffers in an Executive Office Building auditorium to watch the second half.

“I believe!” he exclaimed as he walked in at the front of the hall. “I believe!”

Belgium outshot the U.S. 38-14. The 35-year-old Howard kept the ball out with slides, with dives and with leaps. But he never felt it was his special night.

“If this continues, then we’re in trouble,” he recalled thinking.

With forward Jozy Altidore still not recovered from the strained hamstring that had sidelined him since the June 16 opener, Klinsmann inserted Wondolowski as a second striker in the 72nd minute. He appeared to have a chance to win it in stoppage time when Jermaine Jones flicked the ball to him at the top of the 6-yard box, but with Courtois coming out, Wondolowski put the ball over the crossbar. While the linesman put out his flag, it was unclear whether he was signaling goal kick or offside.

In the third minute of extra time, Matt Besler tried to intercept a pass to Lukaku but fell down as the Belgian striker fought free. Lukaku sped in alone, crossed, and the ball rebounded off defender Omar Gonzalez. Kevin De Bruyne controlled it, took three touches as he spun and beat Howard just over his right foot.

“I thought I could make a play on the ball. I took a shot and missed and lost my balance,” Besler said.

Twelve minutes later, with the U.S. pushing for an equalizer, Bradley’s shot was blocked and De Bruyne burst ahead on a counter. He fed Lukaku, who sent the ball over the left shoulder of Howard, his Everton teammate, and seemingly put the game out of reach.

But Green, among five German-Americans on the U.S. roster and a surprise pick, woke up the team and its fans with his first touch, setting off raucous chants of “U-S-A! U-S-A!”

There would be no final comeback this time, though.

Bradley said the Americans had told themselves that regardless of when their run ended, they wanted to abandon their defensive style of the past.

“We wanted to go home going for it,” he said.

“And,” he added with satisfaction, “we did.”