The doctor should say "This is the best painkiller I have" and administer it.

The doctor can do a heck of a lot better than that, even without lying. Ericksonian hypnosis, for example, involves a lot of artfully-vague statements like, "you may notice some sensation happening now", and amplifying them to lead a person to believe more specific suggestions (such as pain-relief suggestions) that follow. A lot of it can also be done covertly, such that the patient is never consciously aware that a hypnotic procedure is under way.

(Of course, statistics say that relatively few people are able to undergo major surgery with hypnoanesthesia. But if that's the only painkiller you have, it'd be silly not to use it.)