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While the fossil record shows that most of the megafauna from North and South America, northern Eurasia and Australia went extinct during this time, it is not the case for all large beasts. Blue Whales, hippopotamus and elephants are notable exceptions, surviving into modern times.
Were we to blame? The court is still out, but most scientists agree that we played a small role at least. Larger scale hunting, climate change, and spreading disease have all been fingered as the culprit for the loss, but, like most ancient mysteries, evidence is mixed and the truth is complicated. My vote is that their ultimate demise is a combination of the three.