The phrase "narrow sense" means a very specific or limited meaning or interpretation of something. It suggests that the subject has a more precise definition or understanding rather than a broad or general one. Full definition
So you are a believer in only a very narrow sense, and are therefore not very far removed from those who don't believe in any gods at all. (religion.blogs.cnn.com)
A diagnostic term formerly used in a general way to designate the most severe psychological disorders; now used in a much narrower sense in connection with specific symptoms and conditions. (psychology.jrank.org)
But, still, a chance of controversy comes up over the word «divine,» if we take it in the definition in too narrow a sense. (religion-online.org)