Hi,
Use a knife to remove the burned fiber.
Saturate the burn area with glue and then use tweezers to place the carpet fibers on top of the glue. You can use waterproof cement. Leave it to dry for sometime.
Damaging of carpet through a burnt cigarette is not a small problem, I would recommend you to contact to expert professional cleaners in the serious situation.
Thanks,
professional
Carpet Cleaning Chester