If we were following the naming practice which leads from stone to copper to bronze to iron, and distinguishing societies by their cutting-edge technologies (pun intended) then perhaps we might call Rome part of the Steel Age. Their military did after all use Noric steel for weaponry (though how widespread its use was I'm not sure). But steel of one description or another was being made long centuries before that, in Moravia, in Iberia, in East Africa: were they therefore more "advanced" than Rome? Besides, steel does not seem to have been as fundamentally transformative a technology as iron had been. In many ways we might say that the Iron Age was alive and kicking at the Battle of Hastings and even beyond. But we don't.
Besides, no one does talk about the Steel Age. With the Romans, we move to a different system entirely, based not on technology but taking classical culture itself as normative. The classical age, the Middle Ages, the Renaissance, even the Modern (which was at first used as a point of contrast to the Ancients - i.e. Greece and Rome) all use classical Rome rather than any technology as their ultimate point of reference. Only since the industrial revolution have we begun to name ages after technology again, and then only in certain contexts: the railway age, the computer age, the internet age, etc. These may or may not stick: it's up to future archaeologists, I suppose.
Was I going somewhere with this? If I was, I forget. Anyway, feel free to leap in.