There are actually two questions here. Before we can address why the Creed says (or doesn't say) what it does (or doesn't), we need to know what Nicene Christians believe about the substance of the Holy Spirit.
Is the Holy Spirit of one substance with the Father?
The answer seems to be "yes". Consider:
The Athanasian Creed is somewhat more explicit, demanding that when we think of the Trinity, we "neither confound the Persons, nor divide the Essence". (Though often translated "essence", the original Latin is "neque substantiam separantes", where "substantia" is equated to the Nicene "ousia"... and, confusingly enough, is sometimes translated "substance" elsewhere within the Athanasian Creed itself). However...
Why doesn't (e.g.) the Nicene Creed clarify this?
Careful inspection of the above sources reveals that the debate over the consubstantiation of the Holy Spirit seems primarily associated with the Macedonian / Cappadocian split, which was roughly contemporaneous with the Council of Nicea. That is, at the time the Nicene Creed was being formulated, consubstantiation of the Holy Spirit was still being contested. Thus, one possibility is that the authors of the Nicene Creed chose not to make a stance on this particular issue.
However, another possibility is that it wasn't seen as crucial. While they certainly contain broad descriptions of the Christian Faith, the Creeds (in particular the later Nicene and Athanasian creeds) were formulated to address specific issues. It's also possible that the authors felt that consubstantiation of the Holy Spirit was an obvious conclusion when consubstantiation of the Son was established, and therefore felt it unnecessary to belabor the point.
Without explicit writings from the authors themselves, we really can't be certain why the Nicene Creed doesn't specifically mention consubstantiation of the Holy Spirit.
