read the label on the paint tin, use the solvent/product recommended for cleaning used brushes (unlikely to be water - latex isn't water-soluble) However, be prepared for some pattern discolourisation - the solvent could affect the carpet dye (but it will shift the paint!).
Have you tried buying a freezer spray from a plumbers merchant.Spray the stain and it should crumble away.If it hasn't gone deep into the pile try rubbing it with coarse sandpaper.I'm a painter & decorator & have used this method many many times.