SALVADOR, Brazil >> It felt as if Tim Howard would never go down. As if the United States would never go down, standing there, taking shots like an undersized fighter clinging to a puncher’s chance. Howard saved with his hands, his feet, his legs, his chest. At one point, Howard even had a shot bounce off the crest over his heart.

Trying to figure out where soccer fits into the fabric of America is a popular topic, but, for one afternoon at least, there was this unexpected truth: All around the country, from coast to coast and through the nation’s belly, sports fans of every kind were inspired by the performance of a soccer goalkeeper. In a loss.

The ending was cruel, but then so is the game. The United States’ captivating run in the World Cup ended here, on the coast of Brazil, as Belgium beat the Americans, 2-1 after extra time, to eliminate the U.S. A win would have sent the Americans to a mouth-watering quarterfinal against Lionel Messi and Argentina on Saturday; this loss, instead, sent them home.

"It’s heartbreaking," Howard said afterward. "It just hurts."

Of course it does, if only because the U.S. somehow managed to tiptoe along the precipice of glory even as it endured an unyielding Belgian barrage. Howard, who grew up in New Jersey and played in Major League Soccer before moving to the English Premier League in 2003, made 16 saves, the most by a goalkeeper in a World Cup game since 1966.

Yet even with that incredible imbalance — the U.S. managed just 14 shots to Belgium’s 38 — the Americans will rue a missed opportunity to win in regulation (when Chris Wondolowski missed an easy chance, although there was lingering confusion about whether there was an offside call) and a golden chance to force a shootout in extra time (when Clint Dempsey was stopped from 5 yards out by the Belgian goalkeeper).

Ultimately, there was not enough from the Americans. Three draining group games in far-flung locations — including a trip to the Amazon — left the team gasping for air at the finish. Romelu Lukaku, a substitute, scored for Belgium in the 105th minute, and his goal proved to be the difference.

"We were running on fumes," defender Matt Besler said.

When it was over, the fans at the shimmering Arena Fonte Nova applauded knowingly, as if paying tribute to the ride this team provided. The ride had been incredible: Americans purchased more tickets to games here than fans from any country other than Brazil, and television ratings in the U.S. blasted through ceilings, surpassing those of the NBA Finals or the World Series.

Watch parties, too, popped up in places far more varied than just craft breweries, with fans gathering everywhere from Hermosa Beach in California to a library in Birmingham, Ala., to the Tulsa Drillers minor league baseball stadium in Oklahoma. A gathering at Grant Park in Chicago on Tuesday was moved to nearby Soldier Field to accommodate a crowd reported to exceed 25,000.

World Cups have been growing in popularity among Americans for some time, but this tournament has felt different. Explanations for the surge vary, with some pointing to Brazil’s time zone being favorable for U.S. viewers, especially compared to South Africa four years ago. Others say soccer’s spike is simply the result of increasing interest among Hispanics and Millennials — in other words, a steady rise in the number of soccer-loving children growing up to become consumer adults.

"These are all young people who grew up with the game, followed the sports, whether it be the English Premier League or Major League Soccer, and they don’t need to be convinced that soccer is a sport that is worthy of their attention," said Don Garber, the commissioner of MLS. "The country has changed. This is a new America."

Statistics seem to support that claim. Roughly 14 percent of people between the ages of 12-24 said professional soccer was their favorite sport, second only to the NFL, according to Rich Luker, who runs a sports research firm. That leads to savvier and more-informed fans who are more likely to continue following the sport even after the pageantry of the World Cup is over.

"Fans are connecting the dots," said Jeff L’Hote, who runs a soccer-focused management consultancy. "One of the great things about the continued maturation of the sport is people know that Messi plays for Barcelona, not just Argentina."

Whatever the theory, the sheer entertainment value of this tournament has surely helped drive interest. Including Tuesday’s games, 154 goals have already been scored, more than the total for the entire 2010 World Cup.

Also, for casual U.S. fans who find watching games end in ties about as appealing as doing their taxes, this tournament has been a revelation: there were only nine draws in the 48 group stage games, or four fewer than the average during the past four World Cups.

The grittiness of the U.S. team has been a draw, too. Drama, in one form or another, has followed the Americans ever since they opened a pretournament training camp in Northern California in early May.

First there was the question about whether leaving Landon Donovan off the roster was a bad mistake. Then came concerns about whether the Americans could win a must-have game against Ghana (yes, barely); whether they could get a decent result against Portugal (yes, agonizingly) and, finally, whether they could avoid a blowout against Germany (yes, mercifully).

"I think every player went to his limit," coach Jurgen Klinsmann said.

Tuesday followed a similarly tense script. Belgium, which won all three of its group games with late goals, was the aggressor from the start, neutralizing Klinsmann’s attempts to open up the U.S. attack with more players pushing forward.

Things got worse for the U.S. when Fabian Johnson, one of Klinsmann’s most reliable players on the outside, pulled up with a hamstring injury and was taken off in the first half.

The Americans spent most of the rest of the game buckled in, holding off an onslaught from the Belgians, with Howard standing squarely in the middle. Making it to extra time felt like a small victory on its own, but then Lukaku’s fresh legs led to Kevin De Bruyne lashing a shot past Howard from close range. Moments later, Lukaku claimed his own goal, too, and the American fans slumped. The players, though, gathered together during the short break between the two 15-minute halves of extra time and steeled themselves for one last burst.

"If we were going home," midfielder Michael Bradley said, "we wanted to go home going for it."

Julian Green, a World Cup rookie, provided a flicker of hope with a smooth volley two minutes into the final period, and with Howard making two more important saves to keep the game in range, the U.S. kept pushing.

The chances were there. Jermaine Jones blasted a shot over the net. A header went awry. Dempsey, at the end of a gorgeous passing play from a free kick, had his attempt smothered just yards away from the goal.

This time, the miracle never came.

At the final whistle, many of the U.S. players collapsed to the ground. Howard did not. He bent at the waist for just a moment, his hands on his knees, but then he stood up. Even then — in defeat, his tournament over — Howard refused to tumble.

Sam Borden, New York Times

© 2014 The New York Times Company