I think it's worth trying to define first what you mean by "imperium". Both Athens and Sparta developed substantial areas of domination and influence, either through conquest, unequal alliance systems, or systems of tribute. At its height, the Athenian Empire covered the entire Aegean, including the coasts of Thrace and Asia Minor. It also had outposts in Western Greece and made a serious attempt to conquer Sicily. The Spartan Empire, which replaced the Athenian one when it fell, controlled essentially the same range of communities as tributary allies, but also included the states of the Peloponnese, which had long been subjected to Sparta in the unequal alliance system known to modern scholars as the Peloponnesian League. These are fairly extensive realms, especially if you consider that Athens itself never had more than 60,000 adult male citizens, and Sparta, in fact, never more than 10,000.

But my guess is that this is not what you mean by "imperium". Neither Athens nor Sparta absorbed and directly governed its subordinate territories. Their empires never became a single realm; they were conglomerates of ostensibly independent states, who were simply forced to share (and pay for) the foreign policy of their masters. Even the colonies settled by Athens and Sparta were technically autonomous, even if it was usually taken for granted that they'd side with their mother cities in war. The actual territory of ancient Athens was small - about the size of the modern country of Luxembourg - and once it was united, there were few further attempts to expand. The Spartans practiced outright conquest a little bit longer, and the area they ended up ruling was substantially larger, but they still opted for unequal alliances rather than conquest from about 550 BC onward.

So why did this happen? Why didn't Athens and Sparta keep building up imperial momentum, like Rome did, and keep adding to the territory they directly controlled?

To understand this, we need to be careful that we don't oversimply the process of Roman expansion. I'm no expert on Rome, but as I understand it, the Romans didn't simply spread across Italy and then the rest of the Mediterranean like an oil spill. They began by asserting their total control over the region of Latium, much like Sparta did with Lakonia, and Athens with Attika. Then they started to conquer neighbouring peoples. However, these peoples were not initially incorporated into the Roman state; like the members of the Peloponnesian League and the Athenian Empire, they were officially "allies", who were allowed to run their own affairs as long as they served their overlords in war. It wasn't until the conquest of Sardinia in the First Punic War that they began to organise subjugated territory as provincia ruled by Roman officials. It took another century and a half and a civil war for the Italian "allies" of Rome to be recognised as Romans and formally incorporated into the Roman state.

These two developments are generally regarded as crucial steps: first, the assumption of governmental responsibility over Rome's conquests, and second, the awarding of citizenship to Rome's subordinate allies. After the so-called Social War, the Italic peoples surrounding Rome gained citizenship and the rights that came with it, securing for Rome an inexhaustible recruitment pool as well as a prize to hold out to potential future conquests. As they expanded, more and more people were incorporated and directly governed rather than simply subjugated, and in the early 3rd century AD all inhabitants of the Roman Empire were formally given Roman citizenship.

Neither of these processes ever got very far in Athens or Sparta. Athens may have merged all of its territory of Attika into a single community, but very few others were ever granted citizenship, and mass enfranchisement only happened twice (with the Plataians and the Samians). During the Athenian Empire, some overseas areas were settled with citizens and brought under direct control, but the majority of the Empire consisted of subordinate allies who were largely left to their own devices. Sparta, meanwhile, never assimilated even the inhabitants of its own territory; all through Sparta's history, Lakonia was populated partly by semi-autonomous communities of freeborn non-Spartans (the perioikoi or "neighbours"), tied to Sparta through military obligations but largely excluded from the rights and privileges of citizenship. As a result, both Athens and Sparta eventually reached a maximum size, and their policies deliberately prevented them from growing further. Lack of manpower and resources for sustained overseas conquest ensured that their empires, even at their height, were relatively small and short-lived.

Why did they stick so rigidly to a policy of exclusion, rather than assimilating others and keeping up their growth? Fundamentally, it's because citizenship in the Greek world was supposed to exclude. It wasn't a fuzzy category that could be stretched to accomodate outsiders. Rather, it was a zealously defended form of privilege. Given the rights and political representation it conferred, granting citizenship to others meant reducing the relative influence of those who were citizens already. No doubt this was also a factor in Rome, but when Rome was confronted with demands from its allies, it eventually relented; Athens and Sparta never did. They persisted in maintaining their state and empire only for the in-group of citizens who could claim that they had always been part of it. By definition, they could not allow others a share. While Rome eventually realised that its empire could extend further and further if others could be recruited for its cause (allowing ever greater wealth, power and prestige to its ruling class), Athens and Sparta maintained their empires for the sake of their citizen bodies, and consequently couldn't take more than their citizens could hold.