I HAVE THE SOLUTION FOR YOU. We have white carpet throughout our home with 2 cats who throw up their food. I have a bottle of "complete" cat stain and odor removal. IT WORKS WONDFULLY. It completely takes out all of the stains. You soak up as much of the vomit, etc. as you can with paper towel or cloth, spray on the solution and wait a few minutes (I also use a soft scrub brush and agitate lightly) then just soak up all residue with paper towels until dry.
You can but this product at Pet Smart and Petco.