Cut the damaged section out with a jig-saw. Cut two pieces of 1X3 wood, 3" longer than than the opening is wide.
Slip the 1X3's into the underside of the opening and screw them in place with deck screws. (drill pilot holes)
Make a replacement patch from some plywood, using the section that you cut out, as a pattern.
Caulk the patch around the perimeter and drop it into the opening.
Using deck screws, screw the patch onto the 1X3's.
It would be a good idea to glue everything before screwing the pieces together.