Hi,

It looks like you need to add more polygons to the object, you're trying to wrap a flat object around a curved object, so make sure the flat object has the same amount of quads vertically and horizontally that the curved one does. count how many quads the area of the curved object has in the area you're snapping to, and then up the amount on the flat object using the split polygon tool.
If you use the wireframe on shaded option in the viewport it can help when modelling to.