This is where language becomes important. Denying that one "may have lost money" is consistent (given certain assumptions[1]) with one "actually lost money".
[1] Generally the semantics for modal claims allows that what is actual is also possible. But, in ordinary discourse, given some principles of conversational implicature, "may" and "actual" can be taken to be exclusive. Sort of like "or" is taken, in ordinary discourse, to be exclusive so "A or B" is equivalent to "A or B, but not both A and B", although in standard logic, "or" is not taken to be exclusive.
Best wishes,
Bob