The solid Earth has tides too. The rock you are standing on rises and falls by around 30 centimetres twice a day, and you cannot feel it because everything nearby rises with it.

Water is only the visible part. The planet itself is elastic enough to flex, and the bulge sweeps round it as the Moon goes over. Nothing tilts relative to anything you can see, so there is no sensation at all — the only way to notice is to measure against something outside, which is what satellites and very long baseline radio interferometry do.