Why do we neglect the protons from water's autoprotolysis?
You could consider them, but what would be the result?

$0.01 M$ of $\ce{HCl}$ with $1\times10^{-7} M$ of $\ce{H^+}$ from water gives you $0.0100001 M$ of $H^+$. Find the pH of this concentration of $\ce{H^+}$ and compare with the pH you would obtain if you used $0.01 M$ directly.

You shouldn't see that the resulting pH differ significantly.