Since it is for ground-in poop, I would really recommend renting a carpet extractor. (Like Rug Doctor). The extractor forces the water down into the carpet and then forces the dirty water back up into the machine, unlike a lot of your regular home carpet cleaner machines, which basically just do a surface clean and you end up with a lot of water left in your carpet (which will then begin to grow mold and mildew...)
(This advice is from a landlord perspective- I have no carpet in my own home since hubby is allergic to mold and mildew. For my sofa I use a Bissell Little Green Machine (smaller than the Green Machine), but I have not been very impressed with it. Lots of water is left soaking in the cushions, giving it a damp wet-dog smell for days. The carpet extractors we rent for our units have gotten carborator and engine grease off the carpets.)
Note: For any wet mess, make sure it gets cleaned up right away- for example if you have a chronic problem with a dog peeing somewhere, and you miss one accident and it sits there, it will soak through to the padding beneath the carpet and then even an extractor won't do any good removing the smell. You'd need new padding then.
But for your small poop mess, I'd still recommend the extractor. Just rent it for one day and while you have it, do the rest of the house too.