Kumagai said that the Asian Football Confederation "have a responsibility" to look after players after Saturday's match was switched from Pyongyang to Jeddah.
Kumagai spoke to reporters in Japan on Tuesday as she was set to leave for Saudi Arabia, just a day after jetting in from her Italian club Roma.
The 33-year-old said "this kind of thing can't happen", referring to the late notice the national team had been given.
Japan's football association had reportedly asked the AFC to move the first leg from the North Korean capital Pyongyang over a lack of operational transparency and a scarcity of flights.
Reports say the JFA did not receive confirmation that Saudi Arabia would be the new venue until Monday night, and the kick-off time and stadium have yet to be announced.
"As players it's our job to prepare for the match but the organisers definitely have a responsibility to make sure we are in our best condition," added Kumagai.
"This can't happen again."
The return leg of the playoff for a place at this summer's Olympics takes place in Tokyo on February 28.
Because of the uncertainty surrounding the first leg, Japan's four England-based players stayed in London until the venue was confirmed, rather than joining the squad in Japan.
Despite the disruption Kumagai said the team "can't end up using this as an excuse".
"The most important thing is for us not to let this stress us out and we must concentrate on the game," she said.
The AFC did not immediately reply to a request for comment.
