First off, there was no such thing as "Greece" whilst the Roman Republic was on the rise.

There was a multitude of indepenent Greek city states, such as Athens, Corinth or Sparta. Sometimes, these would align in leagues like the Achaean or Aetolian leagues, to defend themselves against some kind of threat or threaten some kind of common enemy. (Often, another league.) There was Macedon, the homeland of Philip III and Alexander the Great, which had more or less asserted itself as Greece's overlord when those two ruled, but now was just one of many Hellenistic successor states to the great empire of Alexander. It frequently tried to re-assert its dominance over various cities or parts of the Greek peninsula, leading to many a war. There was also Epirus, an up-and-coming kingdom on the eastern coast of Adriatic, which though it had never been a part of Alexander's domain, firmly stood in the influence of Greek and Hellenistic thought and culture. Finally, we must not forget the Greek diaspora: many a Greek colony had been founded even before Alexander started conquering, on the coasts of the Black Sea, Sicily, southern Italy and even as far afield as France (Massilia) and Spain. (Emporion.)

Southern Italy is particularly relevant to your question: it was so thoroughly dominated by Greek colonies that it was called Megálē Hellás or Magna Graecia: Great(er) Greece. It was this part of the Greek world that first came into contact with the Romans.

Now, as should be clear, none of these parts and entities I named were united. They were forever fighting one another, or the other Successor Kingdoms, or the Carthaginians, or various local peoples. Alliances and leagues were made and broken with dizzying frequency, and nobody was able to assert himself as the undisputed master of the Greek world as Alexander had been. (And even then, he had not ruled over all Greeks.)

So who was going to stop the Romans? Not the southern Greek city states, who were far more worried about their neighbours or the Antigonid Macedonians. Not those of Sicily, for they were preoccupied with Carthage. Not the Macedonians themselves, for they were struggling to hold on to their dominions and at times to even survive against Epirus to their west. Let alone the Ptolemies or Seleucids all the way in the east.

Finally, the Greeks in Magna Graecia did try to stop the Romans, shortly after they had defeated the Samnites. This was very early on in the history of the Roman empire, you should note. There hardly was an empire to speak of. Rome was a regional Italic power, very successful in conquering and integrating their neighbours, but definitely not something that looked like it could threaten the Greek world as a whole.

Despite this, the city of Tarās(Tarentum) asked and got the help of Pyrrhus of Epirus, one of the best generals of his day and commander of one of the finest professional armies in the Hellenistic tradition. All that was "more technologically advanced and had a better knowledge of war" was represented in Pyrrhus' army.

And he lost the war.

Pyrrhus beat the Romans twice, but it's those battles that give us the term "Phyrric Victory." He also got entangled with the Carthaginians in Sicily, and the third battle against the Romans at Beneventum, though still not tactically decisive, proved too much. He withdrew to Greece. Rome was left to rule Italy. Despite all his apparent advantages, Greek military sophistication had proven unable to decisively defeat Rome.

There would be further attempts at intervention. During the second Punic War, when Hannibal was marching up and down Italy, Carthage and Macedon tried to ally against Rome, so as to negate the potential threat. But other Greek cities of the Aetolian League saw Macedon as the greater threat to their survival, and allied with Rome. They occupied the Macedonians until the Romans could win their war against Carthage. Later, when Rome could focus its full attention east, two further Macedonian wars followed and saw the (at this time highly experienced, thanks to decades of war against the Carthaginians) Roman armies again victorious against their Greek counterparts.

Whilst this was going on, the Seleucid empire under Antiochus the Great tried to intervene also. He send armies west to Greece, but the Romans again proved too strong, and his empire was facing many other troubles in the east. Also, the Romans still had other Greeks on their side in all these conflicts. There's a reason that "divida et impera" is a Latin phrase.

By the time Pompey the Great was marching up and down the Eastern Mediterranean, making and unmaking kings and incorporating provinces left and right, it was far too late for anyone to do anything about Rome's rise.

In summary: "Greece" was never united, and never able to truly make a common cause against Rome. Nonetheless, many of the most powerful Greek kings and kingdoms of their day did try to smack down Rome before they became too powerful. All lost.

As Philip Sabin puts it in his lost battles:

Lendon has highlighted very well how Greek authors such as Polybius tended to ascribe military success to better tactics, techniques or equipment, whereas Roman writers like Caesar or Livy were more concerned with the superior bravery and virtus of the victorious soldiers. The evidence of both Greek and Roman battles lends much more support to the Roman interpretation.

(The Lendon he refers to here is: Lendon, E.Soldiers & Ghosts: a History of Battle in Classical Antiquity. New Haven: Yale University Press (1999) )

In other words: being technologically advanced and having a better knowledge of war doesn't seem to really have helped the Greeks. Roman diplomacy, the quality of Roman armies (at a particular high during this time, thanks to the Punic wars, according to Goldsworthy.) and the reserves of manpower Rome had due to their militia system and many allies proved far more decisive.