grass peels off in moist shaded area

I have a patch of backyard that is very shaded under several large trees.  There's some moss and some very fine grass growing in the area, but it is all pretty sparse.  A lot of exposed, moist dirt.

Yesterday I was walking through the yard and I noticed that I can peel off the lawn in very brittle, thin sheets.  The grass doesn't appear to have even penetrated the top of the soil.

Any thoughts on what might be causing this, how to fix it, or what else I might plant there as ground cover?

usually peeling grass that comes up like carpet is due to grubs.  But perhaps you're right that the shade is keeping it from taking root.  I suppose this would happen if what was laid was sod, but otherwise I would think that the shade would just make for sad, spindly, thin grass, not carpet-pulling-up grass.