''The Love Song of J Alfred Prufrock', along with other important poems by TS Eliot, do reflect (a) a sense of general social and moral despair and (b) a cynicism and loss of faith in the post-World War 1 era of western (mostly European) history. I would tend to agree with your point of view, or question, thus.
Prufrock is himself the epitome of this cynical disillusionment-- his actions/deeds, words and thoughts (as given in the text of the poem which Im sure youve read or are reading) all reflect how he feels lost, without any directions and/or meaning in life; how he sees people and his surroundings, how he views society and its material and often vicious demands.
This cynicism and disillusionment is accompanied with a loss of faith. In the aftermath of the great destruction of the First World War, people thought/believed that there couldnt possibly be a 'god' who could allow such terrible event/s to happen and for such a massive loss of human lives etc. Religion and belief thus fell by the wayside for many people in Western contexts. There seems to be, in 'Prufrock' (as well as poems like 'The Waste Land' and 'Gerontion' etc) little or no hope left and no expectation of a better tomorrow, or of an afterlife that is 'paradisical'-- although TS Eliot himself became a Roman Catholic and a firm believer in Christianity and the church as a firm bedrock or pillar for society, and although he pleads for a return (in 'The Waste Land') to Christianity, to solve the mny problems of Western societies, 'Prufrock' is certainly a darker, sadder, less hopeful poem.