Former US president Donald Trump took a swipe at his own country's women's soccer team on Sunday evening after they crashed out of the World Cup on penalties to Sweden, declaring that "woke equals failure."

Despite sealing American glory at the previous two World Cups, the team have become a lightning rod for anger from the US political right, in part because of their advocacy for social justice.

Many conservatives were particularly chagrined by players taking the knee during the national anthem, in protest at the country's record on racial equality.

Their co-captain, Megan Rapinoe, was given the Presidential Medal of Freedom by Trump's successor, Joe Biden.

She was among the players who missed penalties during Sunday's shoot-out, as the Stars and Stripes made their earliest ever exit from a Women's World Cup, after a 0-0 draw in Melbourne.

Trump, who is running for a White House return in the 2024 election, wrote on his own TruthSocial website that the loss was "fully emblematic of what is happening to the our once great Nation under Crooked Joe Biden."

"Many of our players were openly hostile to America - No other country behaved in such a manner, or even close. Woke equals failure," he wrote.

"Nice shot Megan," he added, in a jibe at Rapinoe, the former Ballon d'Or and World Cup Golden Boot winner.

The 38-year-old, a central part of the USA sides that won the 2015 and 2019 World Cups as well as Olympic gold in 2012, is at the tournament for the fourth and final time before retiring.

She was a key voice in the team's battle with the US federation for equal pay and conditions and remains an unflinching advocate on racial equality, as well as issues affecting women and the LGBTQ community.

For so long the face of women's soccer at home and abroad, she was close to tears in her post-match interview after the 5-4 penalty loss.

"I mean, this is like a sick joke," she said. "For me personally, this is dark comedy. I missed a penalty."

Trump, the frontrunner for the Republican nomination in the 2024 presidential election, faces a series of legal challenges ahead of the national polls, including over allegations he tried to subvert the results of the last election.

President Biden's wife, First Lady Jill Biden, offered the team more consolation than Trump did.

"Today, you inspired us with your grit and determination. We are proud of you," she tweeted.

"Always remember that you encourage women and girls everywhere to show up and fight for their dreams."