Good advice from Mark there about sending your resume off anyway - often recruiters seem to want the world, but will settle for a lot less!
Have you done a TEFL course, as that might up your chances. A CELTA will give you the biggest chance of finding work, but an online course (esp if it's 100 hours or more) will definitely give you a leg-up. These sites might help:
Cactus TEFL :: TEFL Course TEFL Jobs TEFL Advice and
TEFL | TEFL Courses | TEFL Jobs | Teach English Abroad | Teaching English As A Foreign Language - Online TEFL.
I'd say though that Japan is one of the harder countries for non-natives to find work. I'd say to start your search in China - demand there is so massive that they'll very often make exceptions.
There's also a group on this community specifically for non-native speakers that you might want to check out:
Non Native Speakers » i-to-i Chalkboard | TEFL and TESOL Community
Good luck!