you can often wet the putty knife to get a smoother finish....apply the filler so it is just above the level of the existing wood..after the filler has fully dried / cured it can be sanded flush...depending on how deep the damage is you may need to apply a couple of coats...some filler will shrink and crack when applied too thick.
a whole nuther option is quik-wood .. a moldable epoxy putty .. dries hard as nails can be shaped and smoothed to where virtually no sanding is necessary . i use on fine furniture and woodwork all the time .
Apply wood filler to fill the holes, let it harden and sand. You might have to do it twice to get a smooth service. After sanding clean and paint.