"Pity me not" begins with an emphatic command. The speaker insists: whatever you do, don't feel sorry for me! The reason she gives seems to be that pity, in the situation she's talking about, would be ridiculous. Why would one pity someone just because the sun had gone down? It does that every day!
But the way the speaker makes her command suggests that there's something more complicated going on here. She doesn't just say, "Pity me not because the sun always goes down at the end of the day." Rather more poetically, she says that "the light of day / At close of day no longer walks the sky."
This personification suggests not just a sunset, but a kind of vanishing sun-god: a human figure that has gone. While there's no direct evidence yet, there's a sense already that this speaker might be missing, not the sun, but a person who was like the sun to her, bringing warmth and light.
Perhaps the shape of this poem also provides a little hint in that direction. This is a sonnet—and a whole lot of sonnets are about love. Even their meter, the regular five-beat da-DUM of iambic pentameter, sounds like a heartbeat.
Here, though, that heartbeat is disrupted. The poem starts, not with an iamb, but a trochee (DUM-da): "Pity." Leaning on that first syllable, the speaker already seems both insistent and upset, thrown right off her beat. Something pitiable to do with love seems to have happened here, even if the speaker demands not to be pitied.