Cut the tips or threads of the burned carpet carefully. Remove only what is necessary.
Mix a small amount of mild detergent and water in a bucket; the exact amount will depend on the size of the carpet burn.
Spot wash the area, dabbing a soft cloth in the solution and rubbing the carpet until it is clean. Do not add any more water to the area or rinse it. Remove excess liquid with another dry cloth.
Rub the carpet with a clean cloth after it dries to make it look as natural as possible. Any low spots in the carpet should not be visible to the naked eye.
Match your carpet to a remnant or extra carpet piece. Measure the area to be patched, and a cut the patch slightly larger, using a box knife.
Place the patch over the burned area and carefully cut the burned area from the carpet with the box knife. The piece you cut from the carpet should be the exact size and shape of the remnant patch.
Remove the patch of burned carpet and discard.
Attach double-faced tape or carpet adhesive to the patch, and place the patch over the hole in the carpet.
Press the patch down firmly. Rub the carpet gently with a dry cloth to fluff the pile and make the patch look natural.