With the game level in the second half after Hibs striker Eoin Doyle had cancelled out Paul Heffernan's opener, the former Partick Thistle player was shown a yellow card by referee Bobby Madden after going down in the box when challenged Killie defender Michael Nelson, the caution taking him over the disciplinary threshold which brings a one-game ban.
Killie boss Kenny Shiels accused Cairney of making deliberate contact with Ryan O'Leary to win a penalty which was converted by Leigh Griffiths in Hibs' 2-1 win when the two sides met in September.
The Hibees playmaker, however, insisted that there was no ambiguity about the claim and even cited Nelson as a witness.
He said: "I don't care what people say, I know it was a stonewaller. I have seen it in the replay and it was a stonewaller.
"The boy caught me. I am an honest player and I asked the boy after the game if it was a penalty and he said yes so that was disappointing.
"Obviously the referee thought it was a dive but it definitely wasn't so I was disappointed it wasn't a penalty."