Only a small set of windows applications run under Wine...
I assume by .exe you meant Windows application. Wine supports a small number of Windows applications by implementing all functions imported from the EXE header, and functions dynamically loaded at runtime. missing the former causes launch problem, missing the later cause runtime problem. Well known applications like Microsoft Office suite (very old version)are supported by implementing functions specifically for it. You may find a simple app you wrote doesn't run on it although an old MS Office suite does. It probably doesn't worth it to put too much effort in it. Constantly get the same error message may be caused by the implementation of the required function is just a place hold, does nothing but return an error (I saw lots of code like that in Wine).
However, this was true 5 years ago. It may worth checking for updates. I would be surprised if the situation is foundamentally changed, given the approach has been used and the huge number of API functions which constantly evolve and expand..