Take a picture of the wood in the ceiling that you intend to fill.
Find wood putty to match the wood grain. If you cannot find a color that matches the wood, purchase a multipack of wood putty in a variety of colors, and mix putty of different colors to match the wood.
Fill the damage halfway. Use a putty knife for large areas, a pencil to fill deep holes and a flat-head screwdriver for shallow, small holes. Allow the putty to dry for 30 minutes. Then check the color. If it does not match, mix again to find a closer match. Then fill the rest of the damage. Add a little bit more than it takes to fill. Gravity will not be a problem because wood putty is designed to cling. Once pressed into the hole, it will not fall out. If you are concerned that it might, cover the puttied area with plastic wrap held in place with duct tape while they putty dries. However, dry or moist (some putties are not designed to dry out completely), the pliable putty will cling to the wood fibers.
Allow the filler to dry for 30 minutes.
Sand the putty flat with fine sandpaper.
Wipe the ceiling surface clean with a tack cloth. Sweep or vacuum the sanding dust from the floor.