How can the Moon have such a strong effect on the ocean? The gravitational acceleration on Earth is approximately $ 10 \mathrm{m}/\mathrm{s}^2 $.  Compared to this, the tidal effect of the Moon's gravity gives a local variation in the acceleration of approximately $ 9 \cdot 10^{-7} \mathrm{m}/\mathrm{s}^2 $, that is, seven orders of magnitudes less.  The level of the water can rise $ 1 \mathrm{m} $ during high tide, which is only three and a half orders of magnitude smaller than the depth of the ocean.  
How can this small variation in gravity move so much water and cause such a strong effect on the seas?  
 A: The relevant "100%" from which you should calculate the percentage isn't the depth of the ocean but the radius of the Earth 
$$ R\sim 6,378,000\,{\rm m} $$
Multiply this $R$ by $10^{-7}$ and you will get $0.6$ meters, a reasonable estimate for average tides.
You must understand that the surface of the ocean always tries to create an "equipotential surface" – connect all points that have the same gravitational potential. The Earth's gravity (plus the centrifugal potential) adds the major contribution to the potential and, as you said, the Moon modifies this function by corrections that are 7 orders of magnitude smaller and that are anisotropic (different in different directions). That's why the ellipse we get because of the Moon will differ from the previous one by corrections of order $10^{-7}$, too.
For example, if you imagine the Moon-less Earth to be a sphere, its ocean is spherical, i.e. ellipsoid with semi-axes $a=b=c$. A correction to the original potential that is 7 orders of magnitude smaller will create $|a-b|/a$ of order $10^{-7}$. All these calculations may be done much more accurately although the precise shape of continents etc. is needed for learning the precise shape of tides at various points of the real globe.
Whether there is 100 meters of water, 11 km of water, or (unrealistically) 3,000 km of water beneath a point on the ocean surface plays no role in the fact that the ocean will be elevated or suppressed by a few meters or so.
