I used a can of Spot Shot when my DH left a wet box on our new carpet and it left black ink everywhere. It worked great, no stain.
I also heard but have never tried using an iron and dawn dishwashing soap.
I googled it and here are the instructions:
Start with Dawn dishwashing detergent - the original blue type. Add five or six drops to two cups of warm water. Dampen a white cotton cloth with this solution and lay it over the stain. Then place a clothes iron on top of it, set on "low".
Let this sit for fifteen minutes, and don't press down. The red stain will start to wick up into the cloth. You should see red on the cloth. Fold it to use a clean part or apply a new cloth, and repeat the process.
It takes patience to get red stains out of carpet, but even year-old Kool Aid stains have been removed using this method. Repeat the process again and again until there is no more transfer of the red stain to the cloth. Rinse the spot with water, blot it up, and dry it quickly. Quick drying prevents any stain deeper down from wicking up to the surface.
To summarize: use clean white cotton cloth (several), low heat, and don't press or rub. Let the color wick up into the cloth at its own rate, then rinse and dry the area quickly. You can, at the very least, lighten Kool Aid stains and other red stains in carpet using this technique.
Good Luck.