My Pet Peed was designed to be a spot treater and wasn't designed to be used in a carpet cleaning machine. But it can be done.
NOTE: I ALWAYS recommend that you spot treat the hot spots FIRST, then once you get these areas clean you can come back over the entire room with a carpet cleaning machine and MPP'd to "freshen" the carpet up.
The two tricks are:
1) Do not dilute the product. You need to use it straight
2) Do not use the suction feature on the machine. MPP's works best in the first 2-6hrs after application, and will to continue to work for up to 24hrs.
So you can use the machine to apply it to the carpet evenly, just don't pick it right back up, in fact you just let MPP'd evaporate and air dry.
Here is a full blog post/video on how to do it: http://www.mypetpeed.com/how-to-remove-pet-stains-from-carpet-using-a-carpet-cleaning-machine-my-pet-peed-pet-stain-odor-remover/
How I do it:
We have 4 dogs and a pool so our rugs always start to get that wet dog smell. This is the perfect scenario for using a carpet cleaning machine to apply MPP"d; it isn't really an accident area, the whole rug just kind of stinks.
So about 2-3 times a year I use a gallon to clean each 10'x14' rug. The gallon (used as directed above) will list about 3 applications on this size rug, so I usually just spread the applications out over a day or so, giving the product at least 6hrs to work between each applications.
NOTE: Using this much product will make the room smell HORRIBLE. This is normal (and temporary), it is just the airborne bacteria (literally "dirty air") from what MPP'd was able to break down and extract from the rug. I usually just get some fans to pump in fresh air and push the old/dirty air out to speed up the process.