It's pretty common to hear that people in western Europe reacted to the Plague like it was the end of the world, but I think this is very hard to internalize for us. Death rates in cities could spiral as high as 90%. Think of say, your immediate circle of ten friends, maybe twenty - they would all be dead. Go on facebook, look at your friend total, chop off a zero. There was a real and visceral fear that this was the judgement of the world, and that world was most certainly found wanting. The closest modern equivalent is the fear of nuclear holocaust in the 50s, a relationship that Ingmar Bergman's Seventh Seal captured quite well.
The effect on the "power of religion" - if such a thing could even be mentioned - was varied. Yes, lots of people looked to the Church for relief and salvation, but the state of the Church in the mid-fourteenth century wasn't so hot. The papacy had left Rome and been set up in Avignon for almost fifty years, and this was seen as additional reinforcement of apocalyptic expectations.
The book to read is: