The word you require is in the quote you have used - Reduce
Merriam-Webster
1b (2): to decrease the volume and concentrate the flavor of by boiling
add the wine and reduce the sauce for two minutes
Collins
5: If you reduce liquid when you are cooking, or if it reduces, it is boiled in order to make it less in quantity and thicker.
Boil the liquid in a small saucepan to reduce it by half. [VERB noun]
Simmer until mixture reduces. [VERB]
can I say "I boiled water down to the bottom of the pot"?
No, as other answers point out, it would mean boil/reduce until all the water has evaporated.
You could say:-
"Reduce the liquid/sauce to the required consistency"
or
"Simmer until the volume of sauce/liquid has reduced by 75%