Jisho

Where did it come from? 落ちる can have many meanings, so it's hard to say specifically what it means with no context.

呆気ない means "abrupt" or "over too quickly" or "less than expected", something along those lines. Here it modifies 落ちる, which can mean "to fall" in a literal sense, but it also has many more abstract meanings.

The complete sentence is: あいつが呆気なく落ちたのがわかるくらい美人でびっくりしたよ。

From that sentence I'd say it's the "fall in love" meaning of 落ちる.

And yeah, just to put it together with 呆気なく, it means something like "all to easily fall (in love)" in that case.

Bleh... I hate that you can't edit here... "All too easily fall (in love)".

Oh, thanks you very much!!