"That's my ask of everybody. As professional footballers ... we have so much success, we have incredible platforms, I ask everybody here to lend your platform, to lift people up, to use this beautiful game to change the world for better."
Rapinoe said after the ceremony that being able to speak out about issues is more important to her than the award.
"I've been very lucky to have this incredible platform that seems to be growing by the day and I plan to use it to the best of my ability," she told reporters. "The award's amazing, of course, but I don't do this for individual awards, certainly not.
"Even the team awards, the World Cup's obviously incredible to win but when we sort of all look back on it, it will be the way we've changed the game and moved the game forward and really been a part of changing the world, this incredible movement that's happening right now, that we'll all be most proud of."
Messi's award moved the Barcelona and Argentina forward one ahead of Cristiano Ronaldo. The Juventus forward did not attend the ceremony despite being among the three finalists.
The duo has dominated the award since 2008, with their string of victories interrupted only by Luka Modric last year.
Liverpool defender Virgil van Dijk was the other finalist.
His club manager Jurgen Klopp was named Coach of the Year after steering Liverpool to the Champions League title in June, while teammate Alisson won the Men's Goalkeeper of the Year award.
"I have to thank my team because as coach, you can only be as good as your team," Klopp said.
Ellis also thanked her players.
"I owe so much to them," she said.
Ellis resigned in July, shortly after the US beat the Netherlands 2-0 to win their second successive World Cup.
The 53-year-old Ellis was named coach of the US team in 2014 and led them to eight tournament titles. During her tenure, the US lost just seven matches.
Her players made up nearly half the Women's Team of the Year, with Kelley O'Hara, Julie Ertz, Rose Lavelle and Alex Morgan included in the 11, as well as Rapinoe.
The award for the best women's goalkeeper went to Sari van Veenendaal of Atletico Madrid and the Netherlands who captained her side to the World Cup final.
- AP