Well, it does the job here.
If you apply this CL curve:
you may see that we have tweaked the darkest pixels in the image (look at the lower, grayscale bar), and by dragging them down we have effectively lowered its saturation (look at the left bar).
E.g. This is a crop of an image (original, without CL curve applied):
and by applying the previous curve:
as you may see, the darkest parts of the fruits have been almost completely desaturated
(Don’t forget to turn on the tool)