A thrilling Liberty Stadium encounter ended in a 3-3 draw, a result which had looked unlikely when Stoke roared into a 2-0 first-half lead as Jonathan Walters and Stephen Ireland produced composed finishes.
But Wilfried Bony got one back early in the second half, before Nathan Dyer levelled and the Ivorian struck his 10th goal of the season to put Swansea ahead with four minutes to go.
However, the Swans, who had let leads slip in the dying moments of both Europa League meetings with Kuban Krasnodar, were denied again when Madley, taking charge of only his third Premier League game, decided Wayne Routledge had handled after Steven Nzonzi flicked on a Robert Huth header.
Substitute Charlie Adam made no mistake from the spot as the Potters snatched a point.
Laudrup conceded the ball had "maybe" struck Routledge on the arm, but he was deeply unhappy with the decision despite attempting to be careful with his words in order to avoid any action from the Football Association.
He said: "In every game there are talking points over decisions, but when I saw it again, or even out there, there are seven Stoke players in the box and none were asking for a penalty, apart from Peter Crouch, who was appealing for a corner.
"So there was only one man in the stadium who thought it was a penalty, and unfortunately that was the referee.
"But the referees are not allowed to say anything and I have to be careful what I say otherwise I will get a fine or a sanction.
"Of course we can all make mistakes and say we are sorry, the players can do the same. But we have to leave the referees, it would be nice if the referee said 'sorry, it was a mistake'."
When it was put to him that the ball had struck Routledge's arm, Laudrup said: "Maybe, but it is not always handball if it touches you.
"Whenever there is a handball there are players trying to do something to make the referee give handball.
"But there were seven Stoke players in the box, none of them asking for the penalty.
"It was in the last minute, if Stoke thought it was handball I am sure they would try to ask for it. So why give it?
"It would have been a fantastic win and it is all away because of a very, very bad decision."
He added: "I have not spoken to the referee, I do not know the rules on that so I have to be careful. I have heard you cannot even say a referee is good before the game or you can get fined, so I can't say much more as I don't have £10,000 to waste."
But Laudrup did praise his side's fightback after a poor first-half display.
"I just feel so sorry for my players given how they performed after a difficult start to the game, 2-0 down after 20 or so minutes," he said.
"We couldn't believe it but we continued to play in a difficult situation. We came out in the second half and kept Stoke in their box for the entire second half.
"We scored one, then the second and what should have been the winner, and then this happens in the last minute."
Stoke boss Mark Hughes saw his side's winless run extend to eight league games, but was happy to take a point, although he did have sympathy for Laudrup.
He said: "I have seen it and I can understand why Swansea are aggrieved about it, but those things can go for you or go against you and we are grateful we got a break.
"It still had to be dispatched and Charlie did well as he had not been on long and showed good mental strength to get us a point, which at that stage it looked like we were not going to get.
"In the first half we were excellent, we came with a gameplan and executed it.
"We knew there would be a response, we knew they would put us under pressure, and we could have handled it better.
"To concede three goals in the manner we did was not what we have been about this season."
Source: PA
Source: PA