Neil McCann branded the decision to award Kilmarnock the penalty to give the Ayrshire side a 2-1 lead as a ‘disgrace.’
Steven McLean pointed to the spot after Jordan Jones went down in the Dundee box in the second half but video footage shows that no contact was made by Cammy Kerr and it was an incorrect decision.
"We are told to watch our conduct at the side of the pitch, and it's a very emotional game we are involved in, management. We are told about our comments, how we conduct ourselves against the fourth (official), against the assistant, and the referee.
"Referees, I am told, have to be certain it's a penalty. You can't make that decision if you're not certain.
"And I've just watched it and there's no contact. It's a joke of a decision and it's a pivotal moment in the match, because again we have got to come from behind.
"It's changed the whole outcome of that game, because it's asked us questions against a very, very structured, well-organised side under Steve Clarke. And I'm not taking anything away from them, they defended well. But it helps their cause, and they set up on the counter-attack.
"But the decision is a disgrace and it's really hard right now to control my emotions.
"I went over to Steven after the game and told him that he has to be sure. He just looked at me and I said he can't be sure to make that decision. Because I am looking at that from 50-60 yards away and I can see Jordan has gone down.
"Now players can take a good touch in the box and they are waiting on contact, minimal contact, and they will go down. It doesn't take a lot. There is no contact.
"The defining point for me is he told boys in my team that he has taken a dive. And that's pretty sore to take.
"I asked the boy coming off himself. He just shook my hand, I shook his hand and asked him if he'd gone down, and he didn't answer me. But I don't know if he'd want to answer a manager.
"It's really sore just now and I've told the boys I feel sorry for them because it's a horrible position to be in."