The Romans never really "defeated' the Parthians (or the Persians which preceded and succeeded them). They weren't invincible before Trajan; Marc Antony's legate Publius Ventidius defeated one of their invasions of Syria. Trajan conquered Mesopotamia and took the Parthian capital at Ctesiphon in 115. However, the Romans' ancient enemy had little trouble in recapturing the East, and periodic Roman expeditions had mixed success. The war of Julian the Apostate against the Persians in 363 BC was a catastrophe, culminating in the death of the Emperor. Later, of course, in the time of Heraclitus the Romans lost the entire East to the Parthians, effectively for good (they reconquered it, only to see it fall to Islam a few years later).
Trajan is quite extraordinary -- he pushed the Empire down into the Persian Gulf and dreamed, like Alexander before him, of getting to India. Imagine if the Emperors following him had had the gumption to do so, and Roman law, discipline was passed onto lands as far east as India. This would have put a more united front against Islam.
The Romans never really understood exactly how far it was to India, and so their logistics always failed. Julian's supply lines were extremely tenuous, and it's not clear that any Roman military occupation would have been able to hold on for any great period of time. The other significant problem is lines of communication, both cultural and governmental. The Roman world enjoyed the use of the Mediterranean, whereby it was possible to get from Gades to Alexandria in rather little time. To have half the Empire rely only on overland communications would have been extremely taxing. (Note that Gaul was well served by rivers, and that the Rhone actually flows into the Mediterranean.)
So it's not a question of gumption - it's a question of logistics. A lasting Roman conquest of Parthia would have been logistically and culturally extremely difficult. Alexander managed to race through and nominally seize the whole region, but what he left behind him was simply a new Persia with a change of dynasty, and which thought of itself as theoretically Greek in outlook. The Romans probably would have been able to do little better.