I've never had a stain that carpet cleaner that I purchased a the grocery wouldn't remove. But then again, your stain could be worse.
I suggest starting with one of the stronger carpet cleaners, maybe the 409 carpet cleaner, (if they still make that). With a spray bottle, spray down a little plain water and use a brush to work the water in a bit. Don't soak it, but get the stained area good a damp. This can let the carpet cleaner soak in a bit better. Next follow the instructions of the carpet cleaner that you bought. After working it in, (probably with a rather stiff bristled brush), use a sponge to pull any left over carpet cleaner out, then go over it a couple of times with a water wetted sponge to get the remaining cleaner out.
As Tom suggested, one of those little Bissle hand-held "steam" cleaners or a Shop Vac would make getting the cleaner out of the carpet easier. Typically, if you don't get all of the cleaner out, the area that you cleaned could mat down or bunch up worse than the rest of the carpet.