Barrett made history for Ireland, scoring the winner as a substitute in their 1-0 victory at Scotland in October, which secured their spot at the tournament.
"That's the ultimate hope, that we can increase that, (legacy) but not just for the women's team," she said in an interview with the FIFA website.
"But also for young boys as well, that they have also the aspiration of, 'We've seen the women do it, we want to be able to do it for the men's team as well'.
"And I think with that will come, hopefully, more people involved, better players in the future, and then also more Irish teams at major tournaments."
Barrett warned their World Cup opponents not to underestimate them despite it being their first World Cup.
"We're going to make it very difficult for everybody," she said.
"But again, we're going to also relish the fact that we're there because there are only 32 countries in the world get that opportunity. To be one of them is extra special."
Barrett said that qualifying for the tournament lifted a weight from the team's shoulders.
"We find that we always do well, but had never done enough to get ourselves to that magical place, which is a European Championship or the World Cup. That feeling for everybody was just unbelievable. It really, really was," she said.
Ireland will face Australia in Group B on July 20th before playing Canada and Nigeria.
The ninth edition of the Women's World Cup is being hosted by New Zealand and Australia, with the final scheduled to be played on August 20th in Sydney.