Full Idea
If by "introspection" we mean simply thinking about our own mental states, then there is no objection to introspection, but if we mean a special capacity like vision of looking inwards, there is no such capacity.
Gist of Idea
Introspection is just thinking about mental states, not a special sort of vision
Source
John Searle (The Rediscovery of the Mind [1992], Ch. 6.II.2)
Book Reference
Searle,John R.: 'The Rediscovery of the Mind' [MIT 1999], p.144
A Reaction
This seems to beg the question of how we can be aware of our mental states in order to think about them. One might image that some animals have mental states, but are quite unaware that they have them, because they are totally focused on content.