I think he was criticizing the Narnia books for the ways that they dealt with the religious themes. Fundamentally, they aren't very different from His Dark Materials, but Lewis' way of handling the themes was very cold and proposed answers that Pullman, and probably a lot of other readers, found unsatisfying. In Pullman's books, there are no real answers proposed (though you could argue that the Republic of Heaven is one), and his series could pretty much serve as a commentary and an examination. I'm curious as to what you found un-subtle about the way in which he handled being "preachy", I can't really remember a part in any of the books where I found him being that at all.