Cut a circle through the carpet and around the damaged area with a carpet patch tool. The circular tool looks like a large cookie cutter, but features a razor blade that points downward. Press the tool into the carpet and rotate the tool in a complete circle while maintaining downward pressure, then lift the cut piece away from the floor.
Cut a circle out of a strip of double-faced seam tape with a razor knife. Cut the circle so that it is slightly larger than the opening in the floor.
Peel the tack paper off both sides of the tape.
Fold the seam tape slightly and insert the tape within the hole on the floor.
Cut a patch piece out of the replacement carpet using the carpet patch tool.
Apply a bead of carpet seam adhesive to the edge of the patch.
Press the patch piece onto the seam tape.