not good enough, big enough, skilled enough etc for a particular purpose [≠ adequate]:
The parking facilities are inadequate for a busy shopping centre.
totally/wholly/woefully/hopelessly etc inadequate
The building's electrical system was completely inadequate.
The new air conditioning system proved inadequate.
someone who feels inadequate thinks other people are better, more skilful, more intelligent etc than they are:
The teacher made us feel inadequate and stupid if we made mistakes.
Colleges have been inadequately funded for years.