SALVADOR, Brazil – Goalkeeper Tim Howard played a game of a lifetime on Tuesday night, but even his extraordinary performance could not give the United States a lifeline in the World Cup.

Howard made 16 saves, some of them spectacular, to keep the Americans alive in their Round of 16 match at Arena Fonte Nova, but even the 35-year-old is mortal.

He could not stop a relentless Belgium team from scoring twice in extra time to register a 2-1 victory and eliminate the Americans from the competition.

The Belgians will play Argentina, 1-0 winners over Switzerland on Tuesday, in Saturday’s quarterfinals.

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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 started to be kept at the 1966 World Cup.

But that fabulous 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.”

So the Americans exited the World Cup at the same stage and under similar circumstances as in 2010 — losing in extra time, 2-1. This time they survived the Group of Death, but they felt they could have gone further.

“We can be proud and we can be sad,” center back Omar Gonzalez said. “Our journey ends tonight.”

“Credit to us,” Sounders star and USA captain Clint Dempsey said. “We never gave up, going to 2-0 down. Kept fighting. To this team, a lot of respect because we went down with a fight and we pushed to the very end, and I think they knew that we were the ones who were pushing to get the equalizer.”

Howard did just about everything in his power to keep the U.S. afloat, whether it was parrying the ball over the net or making one of his spectacular kick saves. Probably his best was on Kevin Mirallas in the 76th minute.

“None of that really matters for me,” Howard said. “That’s what I signed up to do, (get) 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.”

Center back Matt Besler said Howard played “unbelievably.”

“Tim played tonight just phenomenal, was outstanding,” USA coach Jurgen Klinsmann said. “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 extra-time periods.

As it turned out, Howard was done in by an Everton FC teammate — forward Romelu Lukaku, who replaced Divock Origi at the start of extra time and who created the first goal and scored the second.

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

“For him to come on so late and for guys who been working their (butts) off, having to chase him around was definitely tough on us.”

Kevin De Bruyne, frustrated by Howard several times, scored three minutes into the first extra period. Lukaku got around 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 a diving Howard to the far left side. Howard fell onto his back in stunned disbelief.

“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 took advantage of those fresh legs, connecting off a counterattack in the 105th minute.

USA midfielder Julian Green, the 19-year-old who has seen action on the Bayern Munich reserve team, made his Cup debut in spectacular fashion, scoring off a 9-yard volley via a Michael Bradley feed two minutes after replacing Alejandro Bedoya.

“It was just phenomenal how he came in and scored that goal and gets us back,” Klinsmann said. “It’s fun to watch that kid grow.”

But for the USA, it was too little and too late.