Lyric discussion by ChristopherX 

Cover art for Sunday Morning lyrics by Velvet Underground, The

People seem unaware of the fact that Reed does offer an explanation of this songs meaning in the live album Max’s Kansas City. “This song is about when you wake up on Sunday and you’ve done something oh so bad and you remember it.” In other words Reed would engage in lamentable activity on Saturday night (drugs and sex for certain) and both praise the fact it was over and lament his behavior on Sunday morning thus:

sunday morning praise the dawning it's just a restless feeling by my side

And

sunday morning and I'm falling I've got {a} feeling I don't want to know

As for the chorus:

watch out the world's behind you (This is the fear of gossip from the act done the night before).

And

there's always someone around you who will call it's nothing at all (This is the optimistic resolution to his mind’s worries. A friend will call and tell him it was nothing which helps put the incident into its proper perspective. Shame resolution was a common theme of Reed’s songs).

Song Meaning
Negative
Subjective
Fear
Regret
Introspection
Anxiety
Reflection
Resolution