Carefully fill the scratched indentation with water, saturating it until it stays wet. This technique is most likely to work if the desk is made of solid wood, rather than particle board or veneer.
Place a damp towel or rag over the scratch and press a hot iron on the rag for several seconds. Repeat if this doesn't work the first time--make sure the water swells the scratch/indentation to make it flush with the surface. Let it dry completely.
Use black shoe polish or a permanent ink marker to very carefully color the scratch. Keep the polish or marker on the scratched area, without scribbling too much onto the adjacent surface.
Buff it with a soft cloth. If the repair looks a little duller than the surrounding paint, buff it with furniture polish.