Professional cleaner here. StarvingButStrong had it almost right. If you use a wetvac, pour a couple ounces of fabric softener in the vac before you start. That’ll kill the suds, so you won’t have a whole roomful of foam. Also, just wet the spot repeatedly with a trigger sprayer. If you soak it deeply, you’ll wet the pad underneath. It’ll take days to dry, and it might go moldy before then. Ick.
There’s nothing wrong with renting an extraction cleaner for this job, if you want to do the whole room anyway. Just start with the shampoo spot, and use plain water and defoamer until you’re done with that spot. Then switch to the regular solution for the rest of the floor. It’s really pretty simple.