Patching a Hold in Drywall

I recently broke my wall, so I had to fix it. I wont go into details, but lets say that someone got mad about something and put a foot through the wall. Anyway, I could have put in backing and cut a new piece of drywall, taped the edged and then finished it. But instead I went the easy route and headed to Lowes. I bought an 8" by 8" wall patch for $5 that doesn't require backing, tape or drywall. I put it up, mudded over it, and scraped away the excess. I'm not a good finisher, in fact I've only done a few small things like this before, so I did my best and then fixed it with sanding 24 hours later. After sanding, I did a second coat, waited 24 hours, sanded, did a third coar, waited 24 hours and sanded one more time. Then I painted with some touch up paint that I had saved. I would have painted the entire wall over to get it perfect, but that would have been too big of a project considering that I will be repainting this room in a few years...