(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.