First of all, don't forget that the sun is 400 times farther from us than the moon is. That fact alone tells us that anything on the earth is attracted to each kilogram of the moon with a force that's 160,000 times stronger than the force that attracts it to each kilogram of the Sun.
But more to your point ... The tides ARE greatly influenced by the sun. That's why tides are considerably higher at New Moon, when the sun and moon are both pulling in the same direction.
