You can make shadows of your own which is what I do.
There might be an easier way to do this, but what I do is just duplicate the character layer, go to blending options- set color overlay to black and then mess around with the opacity and edit-free transform it so that it goes the right way from your light source. You'll probably also have to flip it around a bit so that it fits correctly under your character.
Again, that's how I do it, but theres probably an easier way somewhere

(If you need a more thorough explanation I can rephrase everything to make it easier)
Other then that I loved your idea, just the whole blending it in with the background should be fixed a bit. As long as you keep using photoshop though, you will improve.