How we cite our quotes:
The eternal note of sadness in. (14)
This is the first moment of real sadness in the poem, but it's also a first hint that our speaker is interested in the long view of things. He's not just talking about one night on the beach. He's interested in the "eternal." It's maybe not the most obvious aspect of this poem, but we think "Dover Beach" is about the human spirit, and its relation to the time and space and eternity. Even if the language isn't directly religious, the issues are spiritual.
The Sea of Faith
Was once, too, at the full, and round earth's shore (21-22)
This is the beating heart of this poem, the speaker's diagnosis for what's wrong with this troubled world. Humanity has lost its faith. He looks back nostalgically to a moment when faith was at its high tide, before the sea of faith left us cold and lonely in a dark alley. Of course he just finished pointing out that Sophocles felt the same way, more than 2000 years before. So maybe the speaker's spiritual views are more emotional than logical.
But now I only hear
Its melancholy, long, withdrawing roar, (24-25)
This poem's view of the fate of humanity is all about losing things. The present is a spiritual wilderness, where all we can hear is the long, sad echo of our lost faith. Reading these lines certainly makes it seem like our speaker has lost his faith along with the rest of humanity.