How to prevent users from doing manually what my trigger should do for them?

I have a trigger which inserts a row into a table (table A) based on
what a user inserts into a different table (table B).  To allow this,
the user needs insert permission for table A in order for the trigger
to run.  Is there a way I can restrict this so the user only has
permission to insert via the trigger and not manually?  I can't trust
my users to insert correct values into table A by themselves but I
need them to be able to run the trigger.