Why did Mendeleev not include krypton in his periodic table of 1871?
Because the initial publication of the Table preceded the discovery of krypton by about 30 years.
Krypton was identified by William Ramsay in 1898. Its very name means the "hidden one". As a Noble Gas it is highly chemically unreactive, and would form very few compounds.
Note that from a Periodic perspective, the late discovery of krypton makes sense. Chemical inertness and volatility (i.e. low boiling point) do not lend themselves to chemical identification of an element. Ramsay was probably a VERY accomplished experimenter (so of course was his team); he was a highly deserving Nobel Laureate.