I see plastering/mudding in your future, along with sanding and painting, to do this right.
Personally I'd feed one, two, or three pieces of glued backing board into the hole, and pull them against the inside of the drywall. They could be MDF or scraps of drywall. A C shape may work too. This would provide a lip for you to plaster against. Leave enough space between them for your mountbox to slide through (ie the same size as the hole you should have cut.)
Once they're firmly dried in place, apply mud/plaster to the lip to build it up. You might need multiple layers because of the thickness. Aim to bring the level even with the wall but no more. Remember to allow each layer to dry completely.
Once you hit the right level, sand the plaster. You're aiming to match the texture of the existing wall.
At this time you should also drill the plaster and backing plate for screw holes ready for your mountbox. The backing board should take the thread if you drill the correct sized hole for your screws.
Then paint to match the existing wall. If you can't match the paint, you may need to paint the whole section of wall up to the corner.
Once its dry, continue with your cabling project.
And don't sweat it - these things happen. You've now learned to make the smallest hole you can reasonably get away with :)