Tragedy chants have been around since, at least, the 60's and probably before. They were at their peak in the early 70's and I remember then as a kid 7 or 8 years old, with my mates, taunting Man U fans, on their way to either Goodison or Anfield (we were never fussy!) with a quick rendition of "who's that lying on the runway.." before legging it, hoping there'd be murder after the game, which there usually was.
Fighting chants were always the best though, the classic you've just quoted and the " Your going home in a St Johns ambulance" etc.
Halcyon days...