This story shows you methods for repairing and leveling a hardwood floor before tiling.
Measure the area you have removed and cut a piece of 3/4-inch exterior-grade plywood to the same dimensions. Fit the plywood into the recess, and using a cordless drill, drive 1-3/8-inch coated screws at 3- to 4-inch intervals through the plywood and into the subfloor. Countersink the screws slightly. If your hardwood floor has been refinished, the patch might be thicker than the floor. Use a belt sander to sand the patch until it's level with the flooring.