It sounds like you're trying too hard to match with the singer. You should never do that. Try to find a version without vocal on it, or record your own acoustic version of it.

As far as what you're doing with your voice, you sound really nasally and unconfident. You need to sing with presence and from your gut, not your throat. Don't use your nose to hit the higher notes.

Keep working at it, but don't try to match with what the singer does. Match with the melody of the song instead. I know it sounds like it should be the same thing, but it's not.
Thanks man. Yeah, I get what you mean about the melody thing, I've tried using my own voice, but it just sounds worse. Is there any training I could do that doesn't involve singing lessons and is something I can just do on my own?
I thought it was pretty good, I suck at singing though so I can't give you much advice.

I agree with dmc though, you're coping the singer too much, try to use your own voice.