My own - deeply conventional reading - is that the men going off to war and dying was the cause and the girls picking flowers to put on their graves was the effect.

I would concur with this reading (at least of the last verse; the first verse strikes me as more of a standard meditation on the brevity and transience of youth, with no particular blame being attached to the girls).

I'd also add that, as it was written in 1955 (and by an American), I doubt that the war in question is meant to be World War I.