Why is law of mass action only applicable for elementary reaction?
The Law of Mass action states:

The rate of a reaction is directly proportional to the concentration of reactants raised to powers equal to their stoichometric coefficients

This is only valid for elementary reactions since they happen in a single step. As a result, such simple relations hold good. 

But what about the more complicated ones. Certain reactions, like the oxidation of ethylbenzene to benzoic acid using hot $\ce{KMnO4}$ don't happen in a single magical step. They involve lots of reactive intermediates and transition states, so it's basically a bunch of several elementary reactions. You can't consider the whole reaction as an elementary reaction.

But you can formulate a rate equation for non elementary reactions by considering them as a bunch of elementary ones. However such formulations involve knowing the mechanism of the reaction in question, along with other data.