If religion is taken as one of the primary pillars of culture, then it can be argued that the Roman Empire was not a cultural power. The Romans could not win the clash of civilizations in Europe and the Levant. Both halves of the Roman Empire, the Western and the Eastern, lost their dominant religion and underwent cultural transformation before and after they fell.
With the issuance of the Edict of Milan in 313 AD, Constantine the Great made Christianity legal in the Roman Empire. But this did not lead to a significant conversion to Christianity. Paganism continued to be the dominant religion. The number of Christians was very small. The Christian believers were sometimes prosecuted, though the official policy of the Roman Empire was to leave the Christians alone as long as they did not interfere in imperial authority.
In 476 AD, when the Roman Empire fell to the Visigoths, Christianity was still a minority religion in Europe. The Visigoths were devout Christians and under their rule, there was large scale conversion to Christianity. Thus, the fall of the Roman Empire led to the fall of Rome’s pagan religion and the rise of Christianity in Europe. The Roman Gods were forgotten. The Visigoths trounced the Romans on the political and the religious fronts.
In the eighth century AD, Christianity was the dominant religion in the Levant and the Eastern Roman Empire (Byzantine Empire) was the dominant political power. The Romans could not sustain their supremacy in the Levant. Between eighth and the fifteenth centuries AD, the entire population of the Levant converted to Islam and the Byzantine Empire was wiped out.