The Western Empire fell in 410. However, beginning in the fourth century, more and more of the barbarian tribes were converting to Christianity, so a "Holy War" against them would not make sense. The Visigoths, Othrogoths, and Vandals converted to Arian Christianity.
These tribes flourished and spread during the late Roman Empire in Late Antiquity, or the Migration Period. The Visigoths emerged from earlier Gothic groups (possibly the Thervingi) who had invaded the Roman Empire beginning in 376 and had defeated the Romans at the Battle of Adrianople in 378.
In 507, however, their rule in Gaul was ended by the Franks under Clovis I, who defeated them in the Battle of Vouillé.
The Visigoths were pushed into Spain. The first Frankish king who united the French tribes, Clovis I, converted to the Latin Rite in 496 and the religion spread further from there.
In or around 589, the Visigoths under Reccared I converted from Arianism to Nicene Christianity,
The Byzantine Empire fell to the Ottomon Turks in 1453. They recruited to fight them (rather than pray about the end times) and I see no reason to think that the differing religions of the two sides wasn't used to inspire the soldiers.
Possibly what you are referring to is following the Plague of Justinian, the Eastern Empire gave up trying to reunite with the Western Empire and prevent its final, total collapse. Justinian I (482-565) was the Emperor, but also head of the Church in the East not long after the Sack of Rome in 410. He set about a successful military campaign against the barbarian tribes. The Plague of Justinian was a terrible disease similar to the Black Death that hit Constantinople and was believed to be a punishment from God for his marriage to a "dancer." At this time some people did believe it was the End Times. There weren't any more military campaigns, holy war or any form, because the Eastern Empire couldn't financially afford it due to the plague.