Can "mustn't" be used for conclusions?

I heard this sentence in an American film a while ago as I was watching it on DVD (the part after but is verbatim):

"I'm doing my best but I mustn't be doing it right."

This is something I occasionally hear in American films: phrases like "he mustn't have done it" or "she mustn't be studying now", where a logical conclusion is expressed. So far I've thought that the normal thing to say is "he can't have done it" or "she can't be studying now".

My question is: Can mustn't be used to express a logical conclusion when the speaker is certain that something didn't happen or isn't happening, at least in informal speech? Is this an American usage? (I've never heard this usage in British English, but this doesn't mean it doesn't exist.) Is there a change going on in the usage of the particular modal verb?

Note: All the references I've checked don't even mention this use of mustn't. Google books aren't of help either.

EDIT: I should clarify that I'm asking this question because if I wanted to express that I'm certain I'm not doing something right (as in the sentence quoted from the film) I'd say "I'm doing my best but I can't be doing it right". I would think that the use of mustn't/must not wouldn't be standard usage (although the meaning is perfectly clear to me; I never mistook it for an injuction).

Per my comment, I'd avoid it because it sounds rather dated and "upper class" to me.

Semantically, the reason for avoiding this construction is simply that it takes the focus off the critical word not. Since the "conclusion" clause is intended to convey something along the lines of "I am failing", this negating word is vital to the sense.

In "injunctive" forms, such as "You must/mustn't do that!", the word must is invariably stressed, to emphasise the intended meaning. In OP's usage, the word must wouldn't normally be stressed, because there's no sense of injunction or stricture (except loosely, in the sense that there's a logically enforced conclusion). It's "not doing it right" that counts, which requires not to be vocalised.

To confirm this particular contraction is nonstandard, note just 3 instances of "I mustn't be doing" in Google Books, but 3830 for "I must not be doing" (almost all for the sense relevant here).

I personally find the use of the contraction "mustn't" to be a bit off-putting in this case, but I certainly would have no problem expressing an argument this way:

If John had stolen the money, he would have gotten ink on his fingers when the dye-pack exploded.

John doesn't have ink on his fingers.

Therefore, John must not have stolen the money.

Substituting "can't" for "must not" is valid here, but wouldn't be my natural formulation.

(Generally in this situation, the word not has the same stress as the word must, which is why using a contraction there would sound strange to me.)

The same holds true for situations like this:

"It's supposed to work when I do this!"

"You must not be doing it right".

In that case, saying "You can't be doing it right" would sound very unnatural to me. Or, at the very least, like a Briticism.

I tend to think of "mustn't" as a single lexical unit meaning "must avoid", so if someone said "You mustn't be doing it right", I would first think that they were trying to prevent me from doing it the "right" way.

Several replies here address whether it is appropriate to use the contraction "mustn't" rather than writing out "must not" in such an example. Is this your question, or are you asking about the definition of the word "must"? Assuming the latter ...

"Must" can mean "obligated, required", as in, "You must pay your taxes by April 15", or "You must be quiet while the teacher speaks." That definition doesn't make sense in this context. But "must" can also mean "compelled by necessity, inevitable", as in, "If you hold a rock in the air and release it, it must fall to the ground". The rock is not compelled to fall by the laws of the state legislature, but by the laws of physics.

That's the sense in which "must" is used in contexts like your example. "If A is true, then B must be true" means that B follows inevitably from A because of laws of nature or mathematics or logic. "If the engine is getting fuel, then the problem must be in the electrical system." "Must" here doesn't mean that the problem had better start being in the electrical system or we will subject it to public ridicule or have it arrested. It means that it is (or at least, the writer believes it to be) a logical inevitability.