Ireland finished bottom of their group after losing their opening two games against co-hosts Australia and Olympic champions Canada before a draw with Nigeria - their first ever point at the World Cup.
"With our World Cup journey at an end, the FAI will now undertake a full and comprehensive review of the campaign and tournament, as is our standard practice," the FAI said in a statement to the media.
"This will be discussed at the next FAI board meeting in the coming weeks."
Pauw's contract expires after the World Cup and the Dutch coach said she did not feel like it was her last game in charge and planned to attend the team's homecoming event in Dublin on Thursday.
"Why would I not be at the homecoming? I go back with my team. Otherwise I would have stayed in Australia enjoying the tournament," she added.