The NFHS Mechanics manual, pgae 11: "Remember, an officials count (backcourt, throw-in, etc.) may be used to correct an obvious timing error."

This phrase seems to suggest that the count should be visible, but it does not explicitly say so. I interpret "an official's count" to mean "when an official is counting", which may or may not be visible. Thus, I am allowed to count in my head in this situation and adjust the clock as necessary.

Personally, I have my hand at my side and snap my fingers in rhythm with the clock. That has worked quite well for me judging the release of the last-second shot and correcting a timing mistake like the one in the OP.