In the novelization by James Blish, phasers
were fired into the "maw" only to have the beams "bounce around" inside until their energy was expended.
I know; I know, "not canon!" But it's the closest thing we have to an answer. Maybe such a sequence was intended but for one reason or another (script running over time, not enough money or time to do the added effects) the idea was "cut".
Sincerely,
Bill