Gianni Infantino, the Fifa president, was booed before he handing over the Women's World Cup trophy, and chants of "equal pay" rang out around the Parc Olympique Lyonnais.
Rapinoe, who scored a penalty in a 2-0 win over the Netherlands, is a fierce advocate of equal rights and is leading a dispute between the American players and US Soccer over pay parity.
The 33-year-old said she had no issue with the booing of Infantino as she believes Fifa could do more to promote equality in women's football, claiming: " A little public shame never hurt anybody."
Rapinoe added: "I think everyone is ready for this conversation to move to the next step. I think we're done with: 'Are worth it? Should we have equal pay? Is the market the same?'.
"Everyone's done with that, fans are done with that, players are done with that. In a lot of ways I think sponsors are done with that. Let's get to the next point.
"What's next? How do we support women's federations and women's programmes around the world? What can Fifa do to do that? What can we do to support the leagues around the world?
"We as players, every player at this World Cup, put on the most incredible show that you could ever ask for. We cannot do anything more to impress more, to be better ambassadors, to take on more, to play better or do anything.
"It's time to take it forward to the next step. A little public shame never hurt anybody, right? I'm down with the boos."
Rapinoe was named the player of the tournament for her performances over the past month and was presented with the Golden Ball trophy after the final whistle.
The Reign forward's penalty also ensured that she won the tournament's Golden Boot. Rapinoe finished level with team-mate Alex Morgan and England's Ellen White on six goals, though registered more assists than White and played fewer games than Morgan.
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