If you get slime on the carpet you should immediately try to get most of it up with a paper towel or something to get as much as you can of the slime out of the carpet.
Then soak the area with some vinegar and let it sit on the carpet to work on the slime for awhile.
Usually a couple minutes to 5 minutes is enough and then run some warm water over the area and use a scrub brush to scrub most of the slime out of the carpet and then use a carpet cleaner and run the carpet cleaner over the carpet to clean it up some more.
You might have to go over the area a couple times with the carpet cleaner to get the entire slime out of the carpet but it should work.