Killie chairman Michael Johnston had upset the club's fans by giving Celtic season ticket holders - but not their own supporters - the chance to buy cut-price tickets for the game which was watched by a relatively low crowd of 6,149 fans, most of them in green and white.
Johnston responded to criticism by announcing new incentives for home supporters.
Nevertheless, there was a small protest outside the ground before the game and Johnston accused fans' leaders of attempting to force the club into administration by withholding revenue from ticket sales.
"Their leaders advocate withholding revenue from the club, forcing an insolvency event to try and achieve their objective," Johnston told BBC Scotland.
Johnston, who admitted the timing of the ticket offer to Celtic fans was "regrettable", added: "You hope that people will realise that there's a football match on, with an 18,000-capacity stadium with more than 10,000 empty seats and we're trying to sell tickets for a football match to protect 200 employees at Rugby Park.
"My first obligation is towards the employees, which includes 42 professional footballers.
"The ringleaders of the angry fans have their own agenda and they are trying to force change with an objective of community ownership of the club.
"They don't care about the 200 employees we have here - I do - I'm trying to generate revenue, pay wages and keep people in employment in one of Scotland's biggest unemployment blackspots.
"I apologise for the timing of the announcements, because clearly that was a mistake, and that's highly regrettable, but the bottom line is that nobody was prejudiced by the offer made to Celtic supporters."
Killie boss Johnston insists the background bickering had nothing to do with the defeat.
He said: "No, we have just got to concentrate on the football.
"It is easy enough to make excuses and say that makes a difference but it is the football we have to concentrate on and it shouldn't affect the players.
"It is amazing to think we got beat 5-2 there. It was a really good performance but we lost cheap goals."