The speaker of "Sad and Sorry" is carrying a quiet, constant fear: that the people they care about will eventually leave. It comes up "everyday," and that repetition makes the worry feel like part of ordinary life rather than a passing mood. The speaker doesn't think very highly of themselves, listing what they believe they aren't: the nicest, the prettiest, the smartest. Yet they hold on to one simple fact, which is that they love their friends.
The middle of the poem sounds almost defensive. The speaker insists they don't want pity and that they're fine alone, then admits the truth underneath: they just like company. That small confession is the heart of the poem. The speaker also doesn't want to be seen as a "charity case" or a "sorry face," so they're afraid both of being abandoned and of being pitied. The mood is vulnerable and anxious, but also honest. Returning to the opening worry in the last lines leaves the feeling unresolved, as if the fear never quite goes away.