History was out of its reach, but the United States women’s soccer team isn’t leaving Tokyo empty-handed.

In what was potentially their national team swan song in a major tournament, Carli Lloyd and Megan Rapinoe made sure of that. The two elder stateswomen each scored twice Thursday, powering the U.S. to a Olympic bronze medal with a 4-3 victory over Australia that wasn’t as close as the final result indicated.

“That was the U.S. mentality,” Lloyd said. “We played well, we strung some really good sequences together, scored some great goals. And I’m extremely proud of the way we persevered, the way we turned things around. We’re going home with a medal, and there’s no greater feeling than that.”

It was arguably America’s best performance of the tournament, an aggressive and comprehensive victory that was unlike its struggles for most of the Games. The USWNT was hoping to become the first team to follow up a World Cup title with a gold medal, but that dream ended in a 1-0 semifinal loss to Canada in which it outshot its opponent, 13-3.

The disappointment of that match didn’t negatively impact the Americans. Rapinoe, 36, struck first, on a direct corner kick — an Olympico in the Olympics — in the eighth minute. She tacked on another goal in the 21st minute with a sweet volley on a failed clearance by the Aussies.

Lloyd, a 39-year-old Rutgers alum and the oldest USWNT Olympian ever, sent the United States into the locker room on a high during first-half stoppage time. She scored again — her U.S. record 10th career Olympic goal — six minutes after intermission. Caitlin Foord, Sam Kerr and Emily Gielnik scored for Australia, Gielnik’s 90th minute blast creating an uneasy four minutes of stoppage time for the USWNT, but the Americans closed it out.

“It’s very satisfying. I think we all realized we didn’t play the best this entire tournament,” captain Becky Sauerbrunn said. “So to have the response that we did after a very disappointing semifinal, to show the USA mentality and the resiliency, to put the performance in that we wanted to be playing the entire time, and to finally find it in a game like that — very satisfying.”

It is uncertain what Rapinoe’s future holds. For Lloyd, who was making her 312th appearance for the national team, passing Christie Rampone for second on the all-time list, this was expected to be her last major tournament. When she came out in the 81st minute, the USWNT bench gave her a standing ovation.

It was a bittersweet finish for the U.S., the top-ranked team in the world. The Olympics started poorly, with a dismal 3-0 loss to Sweden, snapping a 44-match winning streak. There was a scoreless draw in the group stage with Australia and a shootout victory over the Netherlands in the quarterfinals, prior to the loss to Canada.

Their stay in Japan, though, ended on a positive note, with the type of performance that was expected from them more frequently during these Games.

“We just didn’t have our juice. Making simple mistakes, I think, and overthinking it a little bit,” Rapinoe said. “Eventually we’ll have to do the debrief and figure out why we played five bad games and had one good game in the tournament.”