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.
Cairney 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."
Nelson denied admitting it was a certain penalty although he sympathised with Cairney's yellow card.
He said: "There was contact but how far down he was when the contact was made, I don't know, we will have to see it again. As he slipped the ball to the side he was already going down. It could have gone either way but the referee seen it so I am not going to argue."
Hibs boss Pat Fenlon was more upset by Cairney's impending suspension than the rejected penalty claim.
"I haven't seen it so it is difficult to comment," he said. "But Paul said he caught him and some of the players who seen it on the televisions said it was a penalty.
"These things happen. I am not one to come in and criticise the referee but if he has got it wrong I am sure he will hold his hand up. Maybe I need to moan a little bit more and I might get a few more for us but some of them go for you, some of them don't.
"I am more disappointed with the yellow card because we will lose Paul through suspension and that is more disappointing than the actual decision."
Killie assistant manager Jimmy Nicholl kept his distance from the incident to an extent by saying: "We should have had a penalty in the first half with Sissoko and maybe they feel they should have had one with Cairney as well, I don't know but I will leave the refereeing decisions to the referee."