De l’eau would be the natural expression here. After all, you are not thinking about the abstract concept of H2O, you want to drink some water… However you might want to phrase it, we’ll put some kind of quantifier — un verre d’eau, de l’eau, un peu d’eau, etc. Eau alone would be very weird, and non-native.

The partitive article will still be needed, even in short sentences. Even if you are not actually "talking" but only "thinking in your head".

In the desert, you would indeed beg for De l’eau ! De l’eau ! even in your head. I can imagine a speaker would say Eau ! Eau ! only if he is about to faint and cannot speak properly, so this is really far-fetched, and not standard.

Some other examples:

Tu préfères du vin ou de la bière ?

Du vin.

Not vin alone. Same if you imagine this answer in your thoughts before you actually pronounce the words.

Or, imagine you are in a very secluded room, and you go out because you want to have some fresh air. You will say:

De l’air ! De l’air !

And not Air ! Air !, that would be very awkward.

The only case I can think of would be “terre”, when you’re on a ship and you see the coast you can say “Terre ! Terre à l’horizon !” and you won’t say “De la terre !”

Obviously it’s not the most common thing you may say but it exists !

Partitive articles are quite important in French. Skipping them sounds childish, clumsy at worst.
I think it could be explained as this: If you have an item you cannot split easily (cake, bread, liquid, semi-liquids like jam, meat etc)… de/du/de la arrives.
Du/de might oddly be translated by:a chunk of
I think it comes from Latin, de,…like in de Natura rerum.

If you can take a plain item like an apple:
Je mange une pomme (I’m eating an apple).

If you cannot exactly count it, du/de/des/de la..
Je mange de la tarte aux pommes (I’m eating some apple pie).

Ah, now is fuzzy time:
Je mange une barbe à papa (I’m eating (a) candy floss)
Je mange de la barbe à papa (I’m eating some candy floss)

DE L’EAU!!!!

Definitively.

Without “DE”, it seems more like an order, like “kill/tue” or “eat/mange”