It's fairly obvious that you understand that you're continuing a clichéd trend, but you've done nothing but acknowledge your own artifice.
e.g
"Like so many fictional novels depicted following World War II, there was a nuclear Holocaust"
It's not bad writing - I particularly like the economy of words, not particularly verbose or overly intricate.
I find that framing your story with another's limits your creativity - your creative impetus is limited to the world of the original creator, no matter how wide it may be. To be utterly frank, your story is fairly average; and I wouldn't give it a second glance.