It is more complicated than that. Arian Germanic tribes (followers of the heresy of Arius) conquered the Western part of Rome. Eastern part was destroyed by Muslims many centuries later.
The Eastern part was destroyed by the Roman Catholic Church between 1198-1205 .
Fourth Crusade
Pope Innocent III
This was a great blow to the unity of the Church and played a role in the Great Schism. Innocent excommunicated the Venetians in return.
None of this should have happen and Rome lost a the Cathedral of St. Sophia Constantinople which is now a mosque.
I hope you will check out the links..