To leave it at that means to take no further action or say nothing more about something, but in this context the speaker is saying they weren't stupid enough to leave it at that and not to just stop there and spend more time taking further action which is the opposite.
Consider the statement "Looking out the peephole showed nothing, but I wasn't stupid enough to not just stop there and spend more time taking further action.". Based on this "Looking out the peephole showed nothing, but I wasn't stupid enough to leave it at that." a true statement? Yes, no, or I don't know?