I think 'meh' is truly a leakage from Japanese, the same meaning for the same word is in our language for a long time.
I think that is where 'The Simpsons' got it.
It does not have the same meaning as 'tut', which is just a form of disapproving tongue click in both English and Japanese, but did not become a word here.
In my more nightmarish imaginations, I picture cars and trucks with a button to emit a very loud tongue-click.
I do it with my own mouth when some idiot suddenly turns on a bicycle, at speed, on the wrong side of the road, forcing me to brake my own bicycle, but of course, the idiot never uses the brakes.