Double meaning of てしまいます I learned that can both express regret and having finished a task. How can one differentiate between the two meanings without context ? Example: . - I have finished drinking the water / I drank the water (with a sense of regret) If one cannot differentiate without context, is there a way to make explicit which meaning is implied ?

It only has one meaning: "to do something in an irreversible manner". Applying it to various examples may produce various expressions in other languages. But that's a problem of translation, rather than that of the meaning of the word itself.

In the case of your example, doesn't mean "I have finished drinking the water", (or rather I suspect there are any cases where it means "to have finished something"), but "I drank water", and in this case sense of irreversibility usually reflects that of regret.

This sense of irreversibility is not always rendered into that of regret. For example, is an encouragement or an invitation to do something that would feel reluctant otherwise.