(CNN) -

No guts no glory, or so the saying goes.

But perhaps the vanquished United States soccer team can rest in the knowledge that if the World Cup was decided on guts, it would surely be lifting the trophy in Brazil.

For 120 minutes of Tuesday's ultimately unsuccessful last-16 clash with Belgium, each one of Jurgen Klinsmann's men left everything on the field in Salvador.

From the second the Americans went 2-0 down in extra time thanks to goals from Kevin De Bruyne and Romelu Lukaku, the rearguard started.

Substitute Julian Green's goal offered the nation a lifeline and energized its fatigued players with a quarter of an hour to play.

And you could almost hear the sigh of despair from New York to Nevada as late chances for Jermaine Jones and Clint Dempsey were agonizingly spurned.

The final whistle signaled tumult at either end of the emotional spectrum as Belgium advanced to a quarterfinal with Argentina on Saturday and the U.S. departed.

Beaten, yes, but not bowed.

With every passing minute of its participation in the World Cup, the United States had drawn soccer a little closer to its heart.

And though its harrowing exit will cut deep, if ever there was a football match to ignite one nation's passion for the beautiful game this was it.

Buoyed by progress from a tricky group, if the U.S. thought Belgium might represent a simpler prospect than Germany it took less than a minute to dispel that notion.

The Red Devils poured forward like The Red Arrows in the game's fledgling stages as a pass from Kevin De Bruyne, of German outfit VfL Wolfsburg, sent teenager Divock Origi scampering through on goal.

His effort was powerfully struck but just like a succession of German players had found in their final group game, Tim Howard was in parsimonious mood, and blocked with his legs.

Save for a clutch of enterprising moments in three successful group games, Belgium had failed to live up to its pre-tournament tag of dark horse.

But the Europeans bristled with intent during the opening exchanges, with Chelsea's Eden Hazard prominent in each wave of attack.

The United States would not be cowed though, and created its first openings after 20 minutes.

Dempsey narrowly failed to connect with a corner before a marauding run from Michael Bradley, son of former USMNT coach Bob, presented the Seattle Sounders star with a clear sight of goal.

But just as Howard had in the opening minute, Belgium's goalkeeper Thibaut Courtois was equal to the task.

Respite proved brief though, as Belgium resumed its front-foot role.

Jan Vertonghen was twice involved as the Red Devils spurned a pair of chances in quick succession.

First the defender, who plies his trade for Tottenham in the English Premier League, pinched the ball in midfield and fed De Bruyne but he dragged a shot wide.

Then Vertonghen profited down the left channel but hesitated momentarily before pulling the ball across the face of goal, allowing DaMarcus Beasley to clear from inside his own six-yard box.

The pattern continued after the interval, the USA adopting a more open style than in their previous encounter but at the same time struggling to counter the pace and dynamism offered by Belgium.

Origi again gave notice of his menace by glancing a header from a Toby Alderweireld cross onto the crossbar with Howard reduced to the role of spectator.

Then less than 60 seconds later, Vertonghen again created space down the left flank and wormed his way into the area, prompting another low save from Howard.

Despite being pinned inside its own half for long spells, the United States remained a threat on the counter attack, and from one such downfield break Graham Zusi was inches away from connecting with a volley.

Dempsey also tested Courtois with two attempts from range but in the main, the red wave continued.

Kevin Mirallas was the next man to try and pierce USA's rearguard as he sauntered into the area -- defenders in white petrified of upending him -- before the ball ran loose to Origi.

Yet again, Howard earned his stripes and made the block.

The goalkeeper, a long standing servant of English club Everton, had USA fans in raptures again moments later as he diverted another goalbound effort from club colleague Mirallas after he had sprung the offside trap.

Origi stung Howard's palms with a rifled shot from outside the box before Hazard rippled the side-netting as the pressure intensified with the final whistle in sight.

A measure of the attacking swarm Belgium had adopted came with the sight of captain Vincent Kompany picking the ball up in his own area and charging upfield to prompt Howard into another save, as his flick lurched for the bottom corner.

Deep in stoppage time, the moment the United States had been waiting for arrived.

A knockdown inside the area found substitute Chris Wondolowski eight yards out with only the goalkeeper to beat. A nation held its breath and then howled as he launched the ball over the crossbar.

An incorrect offside flag from the linesman spared his blushes, as the crowd in Salvador roared their approval at the conclusion of 90 minutes.

For those recently converted to the joy of soccer it surely proved how thrilling a scoreless draw can be, but the deadlock was broken a matter of minutes into the added 30-minute period.

De Bruyne played the role of destroyer, dancing away from three white shirts inside the area before angling a shot beyond the seemingly unimpeachable Howard.

When substitute Romelu Lukaku added a second 12 minutes later it appeared as if the game was up. But if anything, the Chelsea striker's goal only served to inspire Klinsmann's troops.

Chasing a lifeline, their game plan went out of the window, an all-out approach paying dividends when teenager Green -- a controversial pre-tournament selection in place of U.S. legend Landon Donovan -- volleyed home superbly to halve the deficit.

From that point on, all hell broke loose.