You can use craft fabric paint. May need to blend colors together to get the color you need. A 50/50 mix of water and paint. Lightly pounce with a small paint brush. Very little paint on the brush. Similar to dry brushing.
Rit dye mixed in water in a spray bottle. Spray lightly on the spot and rub it in the carpet fibers with a white cloth. I have done this on a bleach stain on my carpet in the floorboard I’d my car. It worked well.
A nice area rug.
Depending on the color of your carpet, I successfully covered a very small spot like this using a Sharpie permanent marker.