The sentence could be referring to the other meanings of the word "missed" i.e. 1, failed to reach/meet/attend or 2. feel/suffer from the lack of. It could therefore mean that 1. the speaker did not get to meet 3 students or 2. the speaker felt the absence of the 3 students. The sentence is therefore grammatically correct, but inherently awkward because more than 1 meaning could have been intended. However, in speech, as the context is usually already established, it is normal to use such sentences. The typical meaning of the above sentence would actually be that the speaker did not manage to hit 3 students. (Hence, it seems awkward). It is important to note that sentences often do not stand alone, and the reader (or listener) has to glean the intended meaning by understanding the context in which the sentence is used. Hope this helps.

There were three students missing

i am missing three students

You can say 'I missed three students', though it is probably more correct to say 'Three students were missing' or 'Three students didn't come'. All of them have the same meaning though.