The first sweep of the pestilence in Europe created the most damage and mayhem. There weren't enough living people to bury the all of the dead, and those that were fortunate to be buried were laid in long trenches, stacked around 5 deep. Even with a foot or two of earth covering the corpses, the smell permeated the surrounding countryside.
From a contemporary source:
"Since they [plague victims] received no care and attention, almost all of them died. Many ended their lives in the streets both at night and during the day; and many others who died in their houses were only known to be dead because the neighbours smelled their decaying bodies. Dead bodies filled every corner.... Most of them were treated in the same manner by the survivors, who were more concerned to get rid of their rotting bodies than moved by charity towards the dead. With the aid of porters, if they could get them, they carried the bodies out of the houses and laid them at the door; where every morning quantities of the dead might be seen. They then were laid on biers or, as these were often lacking, on tables.
Such was the multitude of corpses brought to the churches every day and almost every hour that there was not enough consecrated ground to give them burial, especially since they wanted to bury each person in the family grave, according to the old custom. Although the cemeteries were full they were forced to dig huge trenches, where they buried the bodies by hundreds. Here they stowed them away like bales in the hold of a ship and covered them with a little earth, until the whole trench was full."
Boccaccio, Giovanni, The Decameron vol. I (translated by Richard Aldington illustrated by Jean de Bosschere, 1930)
Remember that the clergy performed two exceedingly important functions in early to mid-mediaeval society: The clergy administered to the spiritual requirements of the population, and also to the medical needs. The clergy was educated, and did not entirely consist of fundamentalists loyal only to the Church. The local monks and nuns concerned themselves with their fellow townsfolk, whom they usually viewed as their charges under God. They cared for the sick and for the dying, to ensure that if the person couldn't be cured, then the family had the peace of mind knowing the person would not be condemned to hellfire.
Due to the fact that nuns and monks worked directly with the sick and destitute, a large portion of their numbers died in the pestilence. The Church needed to quickly fill these vacancies, and the best candidates were not always chosen (by this point, the best candidates were mostly dead). Uneducated men were placed in positions of authority, with generally negative results. They couldn't read the Bible, they demanded more pay, and even stopped caring for and about the people they were sent to serve, instead leaving the practice of medicine up to God and prayer.* In subsequent flare-ups of the plague, some clergy deserted their posts. No wonder the people stopped trusting in their Church - the men and women representing God left them all to die!
There are some contemporary scholars that attribute the Protestant Reformation directly to this decline in the quality of clergy. True, right after the pestilence swept through Europe, we had the Great Western Papal Schism
(1378 to 1417) where there seemed to be popes everywhere. The people who had already lost much faith in their previously beloved Church were probably just shaking their heads in sadness and disappointment.
Was this mighty plague the result of the sins of the Europeans? If so, why did half the God-loving clergy die? The patron saints seemed to desert them as well. Flagellants began appearing in the street, naked and whipping themselves to atone for sins. This further disturbed the people, and lead to general unrest.
While early in the pestilence the common thought was that this was God's wrath against the people (October 1348 Edict "Voice of Rama"), the tune quickly changed to remind the populace that God is so great, that we can't know what He is thinking.
Or they blamed the Jews.**
*Francis Aiden Gasquet, D.D., The Black Death in 1348 and 1349, (London: George Bell & Sons), 1893.
**Blaming the Jews for anything bad that happens is historically considered to be a fail-safe. In this case, many Christians (even powerful ones) stood up for the Jewish people, but were overwhelmed by the more powerful Christian leaders who were in deep debt to Jewish lenders, and the uneducated and scared population who was looking for something, ANYTHING, to explain the sudden death of half the population. All over western Europe, Jewish people were accused of poisoning the wells, air, other water supplies, or casting spells. As a result, there was a mass exodus of Jewish people to friendly Poland. (Unfortunately, that's where a whole bunch of their decedents would be murdered in the 1930s and 1940s.)