Idiot
Dumb
noun, な adjective
抜く is "to extract." If you extract yourself for an interval of time from the world, you won't learn anything and become an idiot.
The readings come from the ま reading of 間 and from 抜く.
彼に間抜けな田舎者のお上りさんだと思われたくないの。
I don’t want him to think of me as a stupid country bumpkin.