Must + present perfect in a narration about past events

As far as I understand, the construction must + present perfect is used to make presumptions about past events with the connection to the present:

Look, somebody must've been here - the stove is still warm.

But what about narration which is put in past simple? Can I use the same construction like this:

When I woke up and cast a glance on the ceiling, it must have been the
early morning.

Is it correct?