Howard was named man of the match even though the Americans lost in the round of 16 for the second straight World Cup.
"It's heartbreaking," Howard said. "I don't think we could have given any more. What a great game of football. We got beat by a really great team. It's heartache. It hurts."
Asked about the constant barrage of shots, Howard took it in stride.
"It's my job, that's what I sign up to do," Howard said. "Hats off to Belgium, but we gave a valiant effort."
Belgium's unyielding attacks for 90 minutes on Tuesday only highlighted the great performance of the 35-year-old Howard, but the goalkeeper's teammates finally wilted in the evening heat once extra time came.
Three minutes in, Romelu Lukaku found space on the right and passed into the center. At first, the ball was poked out before Kevin De Bruyne gained possession, and his low shot finally missed the yellow foot of Howard and settled inside the post.
"The levee is going to break at some point," Howard said.
But Belgium's comfortable lead didn't last long, as Julian Green came in and closed the gap with 12 minutes to go and made for a nervy ending. Howard said his teammates' late attempt to rally was something to be proud of.
"What an incredible group. Sometimes when you give your best, it doesn't come off, but I'm proud of this group," he said.
Green's goal shortly after the restart gave the team hope, Howard said.
"We said to try to get a goal, and at 2-1, we put pressure on them. A dream falls short, but we'll never forget this night," he said.
The strong Lukaku, Howard's teammate at Everton last season, was difficult for U.S. defenders to manage after he came on as a substitute.
"He was a handful and created chances, and that's what you want from a substitution," Howard said. "Julian did the same for us."
The previous record for saves during a World Cup match was 13, by Peru's Ramon Quiroga in 1978 against the Netherlands.
U.S. coach Jurgen Klinsmann said Howard was a difference-maker.
"What Tim played tonight was phenomenal," he said. "He had an absolutely amazing match, and you have to give him the biggest compliments in the world."
Michael Bradley credited Howard for giving the Americans hope.
"[He] always keeps us in it. Such a good leader, and we rely on him so heavily," he said.
Howard also received kind words from his opponents, with Belgium defender Vincent Kompany tweeting:
Two words.. TIM HOWARD #Respect #BelUSA
- Vincent Kompany (@VincentKompany) July 1, 2014
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