Why do Americans pronounce the word 'pasta' in such a strange way?

Given the apparent influence of Italian-Americans on American culture it really seems to be a linguistic oddity.

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Can't get the video to play, internet problems here this morning, but since we're not in Italy, we pronounce it the way WE like, I guess. I say "pah-sta".

Got through the video -- did I miss something? I can't find "pasta" anywhere on it.