The Welsh team produced a fantastic second-half comeback to lead 3-2 after goals from Jonathan Walters and Stephen Ireland had put Mark Hughes’ men in charge.
Wilfried Bony scored either side of Nathan Dyer's equaliser to leave Stoke facing defeat at the Liberty Stadium.
The dying seconds of injury time brought the visitors a corner, however, and after a goalmouth scramble referee Robert Madley gave a penalty that Charlie Adam fired home.
Wayne Routledge was the man penalised for an apparent handball, but the decision left Laudrup incensed.
"I have to stand here more frustrated than ever because of a very poor decision," the Dane told BBC Sport.
"I always defend referees and linesmen because they are humans but, now I have seen it, there are seven Stoke players inside the box and none of them asking for handball. Just one in the stadium saw it and it was the ref.
"I have to be careful. We can't talk about them. We all make mistakes but I can admit I made a mistake and the referee can't.
"It is like they don't exist; they can't speak. I have to be careful what I say or else I get fined another £1,000.
"Refs make mistakes; we all do, but at least admit it. I am so frustrated for my players. We had a five-hour flight to come back on Friday and I am really sorry for them."
Laudrup hailed the response of his players after Stoke had surged into a two-goal first-half lead.
"I said to the players we have to continue and believe in what we are doing at 2-0 down, and it was an absolutely fantastic second half," he added.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.