Tolkien used allusion. As you you said, he was not a fan of allegory, as it often just retells a story in a derivative fashion.
One common mistake, for instance, is to say the Lord of the Rings is an allegory for the first or second world war. But it doesn't match up correctly. It does however contain allusions to both wars. For example, the image of the mires with dead bodies that Frodo passes is pulled directly from the artillery holes filled with water and poison gas that Tolkien saw after the Battle of the Somme. In a broader sense, LoTR is about war in general. Mordor and its armies are not Germany, then, but evil and war itself.