Japan’s Saki Kumagai, background, scores the decisive goal past United States goalkeeper Hope Solo during the penalty shootout of the Women’s World Cup championship on Sunday, July 27, 2011 in Frankfurt, Germany.

Frankfurt, Germany ? Amid the sorrow that lingers throughout Japan, perhaps a little joy — courtesy of the determined women on its World Cup team.

They beat the Americans for the title in a riveting final Sunday night, 3-1 on penalty kicks, after coming from behind twice in a 2-2 tie. The star of the shootout was feisty goalkeeper Ayumi Kaihori, who made two brilliant saves in the shootout.

All tournament long the teammates poignantly reminded the world they were playing for their battered country, still reeling from the devastation of the March 11 earthquake and tsunami.

Did they ever.

They held the gleaming trophy high above their smiling faces as confetti swirled around the podium, flecking their hair with gold.

“Before we went to the match tonight we had some commentary on television and we heard comments on the situation in Japan,” coach Norio Sasaki said. “We wanted to use this opportunity to thank the people back home for the support that has been given.”

This was Japan’s first appearance in the final of a major tournament, and they had not beaten the Americans in their first 25 meetings, including a pair of 2-0 losses in warm-up games a month before the World Cup. But the Nadeshiko pushed ahead, playing inspired soccer and hoping their success could provide even a small emotional lift to their nation, where nearly 23,000 people died or were reported missing.

After each game, the team unfurled a banner saying, “To our Friends Around the World — Thank You for Your Support.” On Sunday, they did it before the match and afterward they had a new sign to display: Champion — the first Asian country to win this title.

The Americans found it all too hard to grasp. They believed they were meant to be World Cup champions after their rocky year — needing a playoff to qualify, a loss in group play to Sweden, the epic comeback against Brazil. They simply couldn’t pull off one last thriller.

“The players were patient. They wanted to win this game,” Sasaki said. “I think it’s because of that the Americans scored only two goals.”

While the Japanese celebrated at midfield, the Americans stood as a group and watched.

“There are really no words,” Abby Wambach said. “We were so close.”

Minutes, actually.

After Wambach scored in the 104th minute of overtime to give the Americans a 2-1 lead, Homare Sawa flicked in a corner kick in the 117th to tie it. It was the fifth goal of the tournament for Sawa, who was playing in her fifth World Cup.

“We ran and ran,” Sawa said. “We were exhausted, but we kept running.”

The Americans had beaten Brazil on penalty kicks in a quarterfinal, but they didn’t have the same touch Sunday. Give Kaihori credit for some of that. Shannon Boxx took the first U.S. shot, and it banged off Kaihori’s right leg as she dove. After Aya Miyama made her penalty, Carli Lloyd stepped up and sent her shot soaring over the crossbar. As the crowd gasped, Lloyd covered her mouth in dismay.

Solo saved Japan’s next shot, but Kaihori made an impressive two-handed save on a shot by Tobin Heath.

“This is a team effort,” Kaihori said. “In the penalty shootout I just had to believe in myself and I was very confident.”

Solo came up with a save, and Wambach buried her penalty kick.

But Japan need to make just one more, and Saki Kumagai did.

“It’s tough to do two rounds of penalties,” Wambach said. “The keeper knows in a lot of ways where we’re going to go. She made some great saves.”

It’s been 12 years since the United States has won the World Cup, and this team was certain they were the ones to break the drought. They’d needed to beat Italy in a two-game playoff just to get into the World Cup, then lost two games in a three-month span, an unusual “bad streak” for the defending Olympic champions.

After easy wins in their first two games in Germany, the Americans lost to Sweden — their first loss ever in World Cup group play.

But they rallied with one of the most riveting finishes ever in a World Cup game — men’s or women’s — against Brazil in the quarterfinals. Down a player for almost an hour and on the verge of making their earliest exit ever from a major tournament, Wambach’s magnificent, leaping header in the 122nd minute tied the game.

The Americans beat Brazil on penalty kicks and, just like that, a nation was hooked.

Hollywood celebrities, pro athletes, even folks who don’t know a bicycle kick from a Schwinn were captivated by the U.S. women and charmed by their grit and can-do attitude that is uniquely — proudly — American. Even President Barack Obama was a fan, taking to Twitter himself on Sunday morning to wish the team well.

“Sorry I can’t be there to see you play, but I’ll be cheering you on from here. Let’s go. — BO.”