Seven people - six Leeds and one Burnley supporter - were arrested during and after the match.
Peter Pike, former Burnley MP and Chairman of Clarets Trust, said the behaviour of a small minority had overshadowed the game. He said: “The sort of people who do this are morons and in the minority, of course.
"They aren’t even proper football fans. They weren't even paying attention to the game.
"They don’t go for the football - they go to bait the other side."
The match began with a minute’s applause in honour of Jimmy Adamson with fans from both clubs paying their respects. The Clarets legend, who died last week aged 82, managed Leeds United after leaving Turf Moor in the late 1970s to early 1980s.
“As respects were paid by both clubs in honour of Jimmy Adamson, it is a great pity that disrespectful idiots had to go and ruin it," said Mr Pike.
"These type of people have no respect for anything. "This sort of thing does nothing for the game. It damages football.”
The club declined to comment until the full impact of any damage had been assesed, but it was the last thing the club needed after another home defeat.