Yes, if it's of Japanese origin then you should pronounce it
Ta - like the ta in tack,
Ka - to rhyme with ta
Mee - sounds like 'me' as in I
Neh - to rhyme with the 'de' in delicatessen!.
But expect to get a few suspicious looks from people who are too ignorant to believe that they don't know how to pronounce Japanese words! The number of people I've heard say 'tempyooora' instead of 'tenpura'!
; )