Megan Rapinoe has said US Soccer has done “irreparable” damage to their relationship with the US women’s national team after court papers filed as a part of their defense against the team’s gender discrimination lawsuit claimed that the women were less skilled and have less demanding roles than their male counterparts.

“Yes, to a certain extent,” she said of the damage done to the breakdown in relations. “Is that truly how they feel about 50% of the population that they are supposed to be stewarding into the game of soccer?

“I think that says a lot about how they feel about us.

“It’s undertones and undercurrents, sometimes blatantly, that we’ve experienced before which is why we’ve filed the gender discrimination lawsuit. But for them to go that low and take it there in this lawsuit is not just disappointing for us, but more so for what it says to every other person in the country, every kid growing up, not only girls but the boys as well. You’re not lesser because you’re a girl and you’re not better because you’re a boy as well.”

Speaking after the team wore their training tops inside out in a show of “solidarity” against the contentious filings before their 3-1 victory over Japan ensured they won the SheBelieves Cup with three wins in three games, Rapinoe, whose thunderbolt free kick in the seventh minute opened the scoring for the Americans, described the claims as “unacceptable”.

“We just wanted to do something as team to show solidarity not only with ourselves but with all the little girls that those words were spoken to and the little boys and women out there as well who have been told that they are lesser than, just because of who they are,” she said of their small act of protest.

“So we wanted to do something as a team. We always feel like the most important and the most powerful thing is to play and what we do on the field. I think is the most powerful and inspirational so it actually turned out that the only thing that was truly visible was our accomplishments, the stars on top, so that was a little unintended bonus. But we just wanted to show that that kind of rhetoric is obviously completely unacceptable. I know that we’re in a contentious fight but that crossed a line completely.”

USA manager Vlatko Andonovski said he was aware that something was planned and gave his full backing to the players. “I support their fight and what they believe in,” he said. “It’s what makes them special: they are true warriors.”

Megan Rapinoe celebrates her seventh-minute goal during Wednesday’s match against Japan. Photograph: Matthew Emmons/USA Today Sports

And the backing for the team more widely was evident throughout the SheBelieves Cup celebrations, with ‘equal pay’ chants and messages littering the stands. “It’s lovely,” said defender Becky Sauerbrunn. “They’re supportive of what we do on the field but they’re really supportive of what we do off the field too, and sometimes off-field stuff is just as important if not more important. To know that we’ve got that in our corner is huge.”

Following a backlash from fans, players, and sponsors alike, US Soccer president Carlos Cordeiro put out a statement within minutes of the final whistle in Frisco apologizing for the “offense and pain caused”.

“On behalf of US Soccer, I sincerely apologize for the offense and pain caused by language in this week’s court filing, which did not reflect the values of our Federation or our tremendous admiration of our Women’s National Team,” it read. “Our WNT players are incredibly talented and work tirelessly, as they have demonstrated time and again from their Olympic Gold medals to their World Cup titles.” He also said the USSF was committed to “making immediate changes” and make sure their legal strategy shows the “utmost respect not only for our Women’s National Team players but for all female athletes around the world.”

Ballon d’Or winner Rapinoe though was dismissive of the attempt to backtrack. “That wasn’t for us,” she said. “That was for fans, for the media, for sponsors, because that all sounded pretty similar to what we’ve heard before. You want to talk about hostility? Every negotiation we’ve had those undertones are in there that we’re lesser, every mediation that we had, every time we meet with them and obviously the reason that we filed this lawsuit. So for him to put that out saying sorry, presumably to us, we don’t buy it.“

Striker Carli Lloyd’s deposition – which was revealed in court filings in February along with those of Alex Morgan, Rapinoe and others – went viral for her response to being asked in various ways to frame whether the USWNT could compete against the Germany men’s world champions, the USMNT or US youth teams when she replied: “Shall we fight it out to see who wins and then we get paid more?”

After the victory over Japan she said she was yet to read Cordeiro’s statement but elaborated on her frustrations. “My deposition was three or four hours so I remember a lot of that,” she said. “It’s interesting because I train with the U18 boys at home and I have said that. I’m more skillful than all of those boys there, put together! But they are bigger, stronger and faster. That’s just the way that they are born. As they get older, we just can’t compete with that. That’s science. But from a skill point, I’m better than every single number of those boys.

“If you put more speed and strength in me then there is no doubt that I would be able to fully compete. For me, as somebody who is nearly 38, I am giving those boys a run for their money.“

“Our greatest message will always be what we have done on the field,” added Sauerbrunn, who also said that they have been collaborating with other teams that have challenged their federations. “This group is full of really wonderful, powerful women that draws people. If we keep winning and keep being successful that keeps us relevant and I think that keeps more eyes on our fight as well.”