SALVADOR, Brazil - -- As magnificent as he was Tuesday night, goalkeeper Tim Howard was not perfect.

If he was, the United States would be preparing to play Argentina in the World Cup quarterfinals Sunday.

Instead, the Americans are preparing to go home after Howard, with the help of some of his teammates, held off a relentless Belgium side as much as they could en route to a 2-1 extra-time loss in the Round of 16 at Arena Fonte Nova.

Howard put on one of the most brilliant goalkeeping displays in Cup history. He made 16 saves, the most in 48 years, or since records began to be kept at the 1966 World Cup.

But that extraordinary performance could not wash away the bittersweet taste of defeat.

"We played our hearts out tonight," he said. "Sometimes you give your best and fight and scratch and it doesn't work out. Tonight we gave a valiant performance. It hurts. We dreamed. We fell short of our dream."

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So the Americans exited the World Cup at the same stage and under similar circumstances as in 2010 -- losing in extra time. This time they survived the Group of Death, and they felt they could have gone further.

Howard, 35, did just about everything in his power to keep the USA afloat, whether it was parrying the ball over the net or making one of his spectacular kick saves, probably his best on an onrushing Kevin Mirallas in the 76th minute. Regulation ended 0-0.

"None of that really matters for me," Howard said. "That's what I signed up to do, my face in front of balls. It's part of the job. It hurts when you lose. Whether you had no saves or 20 saves it doesn't mean any more to us."

"Tim played tonight just phenomenal, was outstanding," USA coach Jurgen Klinsmann said. "He kept us a long time in this game. You can just give him the biggest compliments in the world."

After surviving a barrage of Belgian shots -- they outshot the USA, 38-14, while placing 27 on net -- the Americans finally cracked in the two 15-minute overtime periods.

Ironically, Howard was done in by his Everton FC teammate, forward Romelu Lukaku, who replaced Divock Origi at the start of extra time and who set up the first goal and scored the second.

"He was the X-factor for them," center back Omar Gonzalez said. "Coming on so late, he is truly a force to be reckoned with."

Kevin De Bruyne, thwarted by Howard several times, scored three minutes into the first extra period. Lukaku got around Matt Besler, who slipped at midfield. He raced down the right side and crossed the ball into the middle. It went off a defender to De Bruyne, whose right-footed effort beat the diving Howard to the far left side. Howard fell onto his back in stunned disbelief.

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"I'd like to have that first one back," Besler said. "I thought I could make a play on the ball. I took a shot and missed and lost my balance."

Lukaku then took advantage of his fresh legs, connecting with a shot off a counterattack in the 105th minute to give Belgium a 2-0 lead.

USA midfielder Julian Green, 19, made his Cup debut in spectacular fashion, scoring off a 9-yard volley via Michael Bradley's feed in the 107th minute only two minutes after coming on.

The goal certainly made for a dramatic finish. The USA wouldn't give up, pressuring the Belgian net. Chris Wondolowski skied a stabbed shot over the crossbar from close range. Not long after, the whistle blew on Team USA's World Cup.