When you don't use the UV editor, but instead use one of the other mapping options in the Material settings in Blender, no UV coordinates are actually generated... at render time, Blender generates the UV coordinates automatically, based on the selected setting (sphere, box, etc). Because no UV coordinates are actually stored in memory as part of the mesh, there are no UVs to export.
if you want to export with UVs, you either need to create the UVs yourself, or find a script that will create UVs based on the other settings in Blender for you.
If you go into edit mode for your object, select all of the verts, and press the "U" key, you will get a pop-up with a variety of options of how to unwrap the model. that will generate proper UVs for you.