The moon does not have that power.
The sun is much more massive than the moon and exerts more gravitational pull on the Earth, keeping it in orbit around itself, and yet the tides are not attributed to the sun, either.
Experiment: Fill a bathtub with water and place a large, spherical magnet about 33 feet above it. Will the water move? No. The water will remain perfectly still. The mass of the magnetic ball will neither pull on the water with magnetic force or with gravitational force. The water will not move.
Now, get into the bathtub and lie down with your head above the water. Breathe. With every breath you take, you can observe the water move up and down. As you breathe in and expand your lungs, the water rises. As you breathe out and deflate your lungs, the water falls. The movement of the water is due to your breathing. Similarly, the ocean tides are due to the planet breathing, as the Earth expands and contracts.
Experiment: Measure the change in the orbit of man-made satellites as they pass under the moon. Does the moon pull them away from Earth?