Am I the only one that thought it was pretty dumb of the Martians to just forget about all their medicine? They absorbed our blood. It pretty much went, "Ah there we go human blood. Ah crap now I got sick." I mean, I can forgive it for the most part, if their medicine wouldn't work on our viruses, bacteria, or infections.
On that note, what exactly kept any possible Martian illnesses from infecting and killing humanity right back at the end of the story? The 50's movie saying that the "smallest creatures of God's kingdom defeated the invaders" could be taken to mean that He Himself prevented it, but what about the other versions?
That comes direct from Wells. That being said, the emphasis is different: Wells, an atheist, meant it ironically—"Humanity proved itself utterly useless in a panic, and were it not for things like viruses, we'd all be utterly screwed." George Pal, a Catholic, took the quotation at face value, and used it in full Sincerity Mode.
The premise in the book is that the Martians have no resistance to disease because they wiped Mars's native pathogens out thousands of years before. They don't even have digestive tracts for surviving bacteria to live inside.
The Martians have been essentially invulnerable super-geniuses for millennia at this point. They're arrogant enough to believe that insignificant amoeba on the planet where even the dominant species is helpless against them can't possibly be any threat against them. In other words, it's our old friend Hubris.
There's a bit of "truth in television" to the idea as well: the novel was an allegory for British and European colonialism, with human invasions into "primitive" cultures frequently accompanied by comparable run-ins with local diseases (such as malaria) suffered by the invaders.
There's additional "truth in television" in that very useful, utilitarian technologies and techniques become forgotten and lost once they are obsolete. Average First World citizens don't know how to skin animals even though they know intellectually that animals have to be skinned, and that used to be common knowledge three or four generations ago at most. Ancient herbology is making a resurgence due to concerns with modern medicine and side effects, but it's through a smoky haze of uncertainty because we forgot herbology once modern medicines worked better.
It's probably also worth noting that concerns about transmission of alien bacteria are possibly a relatively recent, neurotic, and uniquely human thing based on science fiction of the sort that H.G. Wells first imagined: without Wells pointing the way, we very well might not be very worried today about contaminating the planets we visit with Earth bacteria, or stay awake at night wondering at all the things that might go wrong should we accidentally bring alien bacteria back to Earth from an alien world... without the horror/science fiction Artistic License Biology, why would humans or Martians worry about bacteria that evolved on one world being able to infect aliens from a completely different world?