Answer: Actually, what you did was perfect! I'd rake the debris out of the bare spots so the seeds make good contact with the soil, then broadcast the seeds and top it off with a little peat moss. The peat will help hide the seeds from hungry birds and will help keep the seeds moist so they will germinate quickly. If you have lots of seeds you can overseed the entire lawn. If not, just broadcasing over the bare spots will at least eliminate them from the turf area.
Best wishes with your lawn!
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