The pee deterents are for stopping marking which isn't an accident. Either they are marking because of another underlying issue or they have an accident because they didn't get let out soon enough. It's worth it to figure out why they are going inside, because no-spray stuff will not stop accidents.
That said, there will be pee on your carpet in all likelihood.
Baking soda works for getting dog pee up, but cats...that's rough. Sprinkle a lot and it will draw the pee up and make a lovely yellow pee cake. Then dispose of it, then vacuum, then use your carpet spot cleaner then vacuum again.
For cats, get a black light and wait until night time to find the spots and use the Nature's Miracle Urine Destroyer.
Cats want to go in litter, and under normal circumstances will never go on the carpet as long as they have clean litter available. If you have multiple cats, you should have multiple litter boxes. The general ratio goes: one per cat, plus one extra.
If you've done that and still have a cat peeing on the carpet, the cat needs to be checked by the vet for urinary tract problems. If the cat is healthy in that respect, then the issue is behavioral.
My solution was to never live in a house with carpet again. My life has been a lot better since I don't have to clean carpet anymore.