The mass of all the oceans on the surface of the Earth is estimated to be 1.35 * 10^18 metric tons, or 1.35 * 10^21 kilograms.
The mass of the Moon is estimated to be 7.35 * 10^22 kilograms.
The distance from the Moon to the Earth at perigee (the closest distance) is 363,104 kilometers, or 363,104,000 meters.
If you assume the oceans cover the entire earth (rather than 71%) in a uniform layer, you may consider their gravitation to originate from a point in the center of the Earth (see the link in lemon's comment for a proof). Likewise, the gravitation of the Moon can be taken to originate at a point in its center.
The gravitational field of the Moon applies to the entirety of Earth's oceans, not just to a patch. Tidal forces are caused by the difference in gravitational force distance between oceans facing the Moon and oceans on the far side of the Earth.
Adding the interior radii of the Moon (1,737 kilometers) and of the Earth (6,371 kilometers) to the distance at perigee, changing kilometers to meters, and plugging the other amounts into the formula for universal gravitation, with Newton's gravitational constant expressed as force in newtons:
F = (6.67 * 10^-11)*(1.35 * 10^21)*(7.35 * 10^22) / (363,104,000 + 1,737,000 + 6,371,000)^2 = 4.80 * 10^16 newtons
But 4.80 * 10^16 newtons gravitational attraction between the Moon and the oceans means little by itself, because the Earth's gravitational field also acts on the oceans. Obviously, the Earth's attraction for the oceans is much greater than the Moon's, since the Earth is larger and the oceans are closer to the Earth than to the Moon. Therefore, the Moon's pull on the oceans could be represented as a fraction of the Earth's pull on the oceans, and you'd get an idea of the magnitude of the power that causes tides.
The Earth's mass is estimated to be 5.97 * 10^24 kilograms. I'm going to use the acceleration of gravity at the Earth's surface to compute the Earth's force on the oceans: F = (5.97 *10^24) * 9.81 = 5.86 * 10^25 newtons.
So the Moon's pull on the oceans is (4.80 * 10^16) / (5.86 * 10^25) = 8.19 * 10^-10 of the gravitational force holding the oceans on the Earth's surface. A very tiny percentage of the total combined gravitational force on the oceans causes the tides.