Norwood's late equaliser wrecked Cardiff's hopes of getting back into the play-off pack.
He struck as the Welsh side looked home and dry.
Bluebirds boss Malky Mackay confessed: "We're disappointed after we were leading with 30 seconds to go.
"Coventry are fighting for their lives and kept going to the end.
"Now we've got eight massive games left — starting at Birmingham on Sunday."