*Ich bin eingeschlafen* translates to *I have fallen asleep* (present perfect tense).

*Müssen* is the auxiliary verb to express [epistemic modality][1]: *from the circumstances it seems the only logical conclusion that I have fallen asleep*. The meaning is the same as of English *must* in *must have fallen asleep*.

The combination of auxiliary + present perfect tense is the sentence you already know:

> Ich muss <sub>*(modal auxiliary, finite)*</sub> eingeschlafen <sub>*(past participle)*</sub> sein <sub>*(present perfect auxiliary, infinite)*</sub>.

Note that in English, due to the relatedness of both Germanic languages, it's *exactly* the same -- the modal auxiliary is finite, the perfect auxiliary is infinite:

> He must *(finite)* have *(infinite, otherwise it would be has)* fallen (perfect participle) asleep.

  [1]: https://en.wikipedia.org/wiki/Epistemic_modality