Shannon Boxx, Carli Lloyd and Tobin Heath all missed penalties for the Americans, who squandered dozens of chances throughout the game and blew a lead just six minutes from winning their third World Cup title.
"It's obviously heartbreaking," Wambach said. "Japan played well. They never gave up."
Japan became the first Asian nation to win the World Cup, doing it with its first win against the U.S. in 26 tries.
The Americans had taken the lead in the 104th minute off a header by Abby Wambach. Alex Morgan, who scored the first American goal, came up with a blocked cross and sent it to Wambach, who was camped in front of the goal on the 6-yard line. Standing a head taller -- and then some -- from defenders on either side of her, she needed only to nod the ball into the net.
But Sawa flicked in a corner kick in the 117th minute -- earned after 36-year-old captain Christie Rampone raced to clear Yukari Kinga's chip over Hope Solo off the line.
The Americans got one last chance when Morgan was floored by Azusa Iwashimizu just outside the area in the 121st minute. Lloyd, Boxx and Heather O'Reilly huddled behind the ball before O'Reilly tipped it to Lloyd. But Lloyd's shot was well wide, and Heath couldn't make anything happen with the rebound.
The United States had beaten Brazil on penalty kicks in a quarterfinal that was one of the most riveting games in the World Cup, men's or women's. But the Americans didn't have the same touch Sunday.
"You don't; you can't," U.S. coach Pia Sundhage said when asked to explain it. "Sometimes in, sometimes out."
Boxx went first, and her shot banged off Ayumi Kaihori's right leg. After Aya Miyama made hers, wrong-footing Solo, 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 Heath's shot.
Solo came up with a save, and Wambach buried hers. But Japan need to make just one more, and Kumagai did.