[FrankHudson]

I didn't have any pitch issues listening to the vocal. This is not a song where you need to be bang-on pitch-wise either.

I'm midway between the folks above who said "nice and relaxed" and "put more feeling into it". This song, and the song's narrator is a complex case. First off you've got Jagger/Richards' original, putting on their burlesque of Southern American culture. It's a weird inside/outside game to decide how much of that (darkly) humorous stance to take. What I hear in your performance is you taking and performing the song's story straight/serious. I think that can work, and can lead the song to places the Stones didn't quite take it.

One could play this song as an angry kiss off song. You'd need to put a little more sneer and disgust into it (including perhaps some self-disgust). You dumped me? I dumped you! And besides I don't need you anyway. And besides, that's nothing special, that just the way it always goes.

-OR-

You could follow up with your more laid-back feel. In this case you're leaning more on that "basement room with a needle and a spoon" verse. In which case your narrator is self-medicated beyond care, but hurt. There you'd need to play the hurt and numbness both. Not as showy a job, but tougher to do.