Your tears are far more complex than most people realise. For one thing, they are not just salty water. They contain natural antibiotics to discourage the growth of microbes, proteins that are useful in trapping and sweeping out dust particles and detritus, an oily layer that discourages drying and protects sensitive cell surfaces, and a mucous layer covering the surface of the eyeball, the cornea. The mucus is protective in various ways, and offers a surface which is constantly replaced. As it is removed, it takes away any invasive germs that otherwise could have attacked the cornea or the inside of the eyelids. One's blinking activity sweeps such materials to the corner of the eye, where they dry out and form compact lumps that we shed as the so-called "sleep" which is most obvious when we wake up of a morning.

The dry feeling that you refer to does not necessarily have anything to do with real dryness; it is more likely, assuming that the water contained no muddy particles or other muck, simply a lack of lubrication between the eyeball and eyelid. You can hardly expect anything as functionally sophisticated as your tears to be satisfactorily replaced by even the cleanest plain water, once it has washed out the lubricants and protection.