It's my understanding that the Black Death took ~75 million lives, a death count almost too catastrophic to comprehend even today. How did citizens living in Europe during the time come to terms with the plague? I recently watched Ingmar Bergman's 'The Seventh Seal', and the Flagellant Pilgrims seemed to indicate people saw it as some sort of divine punishment. Were any other explanations held? If so, was the cause perceived differently by different social groups or classes? Did any of these groups find the means to effectively counter the pestilence, or was it simply immune to the period's medical capabilities?
First of all I think your number is a bit off. Europe counted between 75 and 90 million people in 1300, depending on which theories and numbers you adhere to. In 1400 Europe counted between 50 to 70 million, again depending on numbers.
As to your question whether other reasons were given than simply divine power, the answer is yes. Commonly people would blame whatever they thought was wrong with their society at the time. As is a consistent phenomenon in medieval times, of course the Jews were often blamed. Gypsies and travellers were also blamed. Lombards (small loansharks) were also often blamed. Aside from those, starting with the black death we see a sort of rise of mysogynie, which would find its climax in later centuries with witch hunts, but would also already express itself in the literature of the time, in which women lost their "honoured" status (chivalry) and became objects of lust. In some smaller cities even Italian merchants were blamed. Although this was limited to smaller cities where long distance traders were less common (and thus less accepted). It is striking that although these fears were mainly caused by xenophobia, they still had a grain of truth: being scared of outsiders during a pandemic like this was actually not stupid.
Now, your question whether some regions managed to manage the plague: yes. The Southern Low Countries kept rising grain prices, increasing fragmentation of grounds and properties (among many other factors) which meant demand was still increasing. This isn't to say that Flanders and her neighbours weren't touched by the Black Death, they definitely were (Bruges probably lost about 27% of her inhabitants according to a recent masters thesis). They were however, due to the immense productivity of Flemish agriculture in comparison to other regions, the unusually high amount of urbanisation and the wealth this brought (although it also brought a nice hub of victims for the plague), able to "weather the storm".
Edit: seeing as you were speaking of medicine also, it could not be healed by human intervention. If you had the bubonic plague, you had a 30-50% chance of dying. If you had the pneumonic plague, death would follow with absolute certainty within about 4 days.
From works like Boccacio's Decameron to rituals like the Festa della Salute ("Holiday of Health") in Venice, the Black Plage had a profound economic and social impact on society.
I get into the practical "Public Health management" aspects in this answer but the impact on society was much wider.