Microphones at Salford’s Moor Lane ground picked up the disgusting chants during Tuesday night’s first-round tie.
Reports suggest the chants were initially started by a small section of Salford supporters but the Leeds fans responded with a song of their own.
The sick Jimmy Savile chant referring to the paedophile’s crimes forced pundits commentating on the game to apologise live on air.
One commentator said: “Apologies if you were offended by anything you heard in the last few minutes.”
Disgraced paedophile and former BBC presenter Jimmy Savile died in 2011 under a cloud of historic sex abuse allegations and was never charged with any offence.
He was born in Leeds and supporters of the club often use his name as a way to goad opposition fans.
A number of Sky Sports customers voiced their disgust at the twisted chants and took to Twitter to show their anger.
One wrote: “Just watching the Salford v Leeds game and I’m sure the Salford fans have just been singing about Jimmy Savile – think that’s a bit over the top.”
“Sky dubbing crowd noise to lessen the Leeds fans singing”
Sky Sports viewer
Another viewer said: “Sky dubbing crowd noise to lessen the Leeds fans singing.”
Another commented: “Watching Leeds Utd Vs Salford on TV and the Sir Jimmy Savile chants have started (as usual) and the commentator has just said ‘I apologise if you are offended by what you’ve just heard’.
Tuesday night’s clash was the first-ever meeting between Salford and Leeds, with the Yorkshire side running out 3-0 winners in the end.
In 2014 Salford FC was bought by Manchester United’s famous Class of ’92.
Former Old Trafford legends Ryan Giggs, Gary Neville, Phil Neville, Paul Scholes and Nicky Butt are co-owners of the club which was this year promoted to the Football League for the first time in its history.