Power in table tennis comes primarily from timing. Not just timing with the ball, but timing the proper use of each muscle used, in the proper order and duration, while timing all this while also hitting the ball. For example, when forehand hitting or looping, you start with the back leg, then the hips, then the shoulders, then the arm, and then the wrist.
Most players don't do this properly as they "short circuit" the proper muscle timing as they attempt to time the shot to a moving ball. Trying to learn these two together is like trying to learn to ride a bicycle and juggle at the same time. You would do better to learn each separately, and then put them together. Similarly, trying to time all these muscle movements just right and still hit the ball is not easy, unless you were trained properly early on as a kid. In that case, it's probably so second nature you don't even notice it, or realize how difficult this dance of the body is when you have to time it to an incoming ball that you have to then graze with a big swing!
But there's a simple way of developing this proper muscle timing. Like most cases where you have to break a bad habit, you need to break it down to its simple parts. In this case, you could shadow practice, though you might need a coach to help you get it right. But there's another way to get it right - slapping!!! No, you shouldn't slap your practice partner, but what you should do is imagine doing so, and go through the motion of slapping very hard (i.e. use your entire body as in a forehand stroke) an imaginary stationary person in the face with a forehand swing. Why would you do this? The key here is 1) that it's a stationary target, and 2) your body will naturally time the muscles for maximum power, since it's not being short-circuited by the attempt to also hit a moving ball.
Practice doing this for both regular forehands and forehand loops (where your slap comes from below) until you feel you have the muscle timing down for maximum power. And THEN go to the table and practice doing this with a moving ball. I've used the forehand as the example here, but the same principle applies to backhands - give your imaginary partner a big backhanded slap!