Any bass decoupler is basically just a shock absorber. If you have a very thick carpet pad, that will do quite a good job of acting as a decoupler.
However, most subwoofers sit atop some sort of "feet". Some have spikes, others have rubber feet, others have sort of stubby, metal feet, but almost all have some sort of "feet" on their bottom.
What's at work here is the principle of distributing weight. If you were to lie down on a bed of nails that only consists of four nails, you would probably puncture yourself! But lie down on a bed of nails made up of hundreds of nails and your weight gets distributed over those hundreds of points, rather than just four, and you do not get punctured!
When a subwoofer is sitting on its "feet", all of its weight is distributed only into those 4-8 points. As such, those "feet" sink rather deeply into any carpet pad, which ultimately couples the subwoofer to the floor once again!
You will actually get better results using just a thick carpet pad if you have the subwoofer's entire bottom surface resting on the carpet.
Ever had a cat or dog sit on your lap? If they are curled up and laying with their whole body on your lap, they feel quite light and you can sit comfortably with them on your lap. But if they stand up, now all of their weight is only distributed into their 4 paws. Suddenly, even a cat's weight can cause discomfort and their little paws sink into your legs!
Spread out the weight and you lessen the force at each point of contact.
A device like the SubDude spreads out the force and also acts as a shock absorber or a cushion. A thick carpet pad will do the same, but beware of those "feet" that can sink deeply into the pad and essentially couple the subwoofer to the floor below.
As for the misconception that concrete will "shake" less than a wood structure, it simply isn't true. Concrete blocks air-borne sound better than a regular wood structure simply because there is much more mass in a concrete wall. But a dense material actually transmits sound more quickly and easily than a less dense material. Remember, sound is just molecules bumping into each other and passing along energy in the form of vibration. In a dense material, the molecules are closer together, so transmission of sound actually happens faster (the speed of sound depends on the medium and denser mediums have higher speeds of sound) and more easily.
Bottom line, you need to decouple your subwoofer whether you have a concrete floor, a wood floor, a tile floor or any other kind of floor! A thick carpet pad will definitely work as a decoupler, but you have to be sure that the weight of the subwoofer is spread out enough that the pad can effectively act as a shock absorber.