Tuesday night's Carling Cup match between the clubs was marred by United fans singing songs about Leeds fans stabbed to death in Turkey 11 years ago.
Tragedy: The Munich air disaster of 1958, where 23 people died
Leeds fans dragged their club's name through the gutter by chanting about the 1958 Munich disaster.
Malcolm Clarke, of the Football Supporters' Federation, said: 'This crosses the line. It's not acceptable for supporters to celebrate or mock the death of another supporter.
Trouble: Manchester United fans set off a flare inside the stadium at Elland Road on Tuesday night
'Banners or songs or chants, it's all the same. It's all disgusting stuff. I am sure the vast majority of fans of both clubs would agree with this.'
Police in Yorkshire confirmed they are investigating events in and around Elland Road.
Tragedy: Tributes to the two Leeds fans who died in Istanbul 11 years ago
Fans as young as 15 fought outside before kick-off and 21 arrests were made.
Ray Fell, of the Leeds Supporters' Trust, said: 'One set of fans singing about airplanes and another singing about people dying in Istanbul. I find it deplorable. There is no room for these people in our game. People have suffered on both sides of the Pennines and this will bring everything back.'
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