Proper way to protect cables above surface-mounted electrical panel
Surface wiring is often allowed in areas not readily subject to damage. I'm surprised it was flagged. The panel in my unfinished basement from 1993 has a fountain of cables coming out of it and it is (was) considered acceptable. 

I'm no code wizard, but I'd put lumber alongside the cables, flush on the sides of the box, between the box and the ceiling. I'd overlay a small piece of plywood (using screws to keep it removable) and call it done. 

--------------------------- &lt; -- ceiling
   ||    |   |   |   ||
   ||    |   |   |   ||
   ||    |   |   |   || &lt; -- framing lumber with cables between
   ||    |   |   |   ||
   ||    |   |   |   ||
   -------------------
   |                  |
   |                  |
   |                  | &lt; -- electrical panel
   |                  |


Cables need to be secured as they would anywhere in a circuit: Every four feet and within 12" of the box. Since they should already be clamped at the panel entry point, you really only need to staple up near the ceiling. If there's a gap behind the cables where they enter the ceiling, install a board of suitable thickness crosswise behind the cables and staple to that.