One reason that applies to the Greeks in particular is that I'm not sure they were even that interested in territorial expansion anyway. Some civilisations just aren't, content instead to stay put and prosper on a small scale. "The Greeks" is a bit misleading anyway -- really it's "The Athenians", "The Spartans", "The Corinthians", etc., fragmented into city-states linked together loosely, but ultimately being separate entities. When they came together, as in the Aegean League that fought of the advance of the Persians, the Ancient Greeks had a scarily good military strength, but it never lasted long (Peleponnesian Wars), so there was no real prospect of large-scale expansion.
On the other hand the Romans were, or at least became, hungry for more lands and territory. Perhaps partly this was by accident: in the Punic Wars against Carthage it ended up with Rome capturing most of Carthage's lands, but that advance was part of a victory march in some senses and perhaps they just forgot to stop? I'm sure it's more complicated than that.
But anyway, for some civilisations the drive is there, and for some it isn't. The results of that drive, in the case of Rome, was a well-organised and strong army that drove all before it, until geographical features ultimately got in the way, or logistics of the time prevented further expansion.