The Capital One Cup winners had taken the lead at The Hawthorns through Luke Moore but their hosts equalised before half-time through Romelu Lukaku, who later saw a penalty saved.
Jonathan de Guzman was then unfortunate to score an own goal but Swansea substitute Roland Lamah was incorrectly denied an equaliser for offside despite the ball coming into his path off Ben Foster and Gareth McAuley.
A furious Laudrup, who signed a contract extension on Friday, told Sky Sports: "Since I came in last summer, I have always said referees have one or two seconds to make up their minds - like today with the penalty.
"Then we can watch it two or three times, we can say if it was or was not a penalty and we can discuss it.
"But what I do not understand is our disallowed goal. That is not a decision in football, it is a rule. You can never be offside if you receive the ball from an opponent."
Laudrup also said: "Frustration is when you see a disallowed goal like this, because someone, obviously, I do not know, they do not know the rules, or whatever."
No question that was the most shockingly incompetent officiating crew in many years. The West Brom penalty was a lol moment. First the award itself, where the ref allowed a foul outside the box, perhaps trying to play advantage, but then called a non-existent foul inside the box instead of bringing it back for a free kick. The assistant ref also had a perfect view but did nothing. A simple mistake that no professional official should make. Then the penalty. Lukaku was still taking his backswing when Vorm had both feet off the line, and there were at least 6 players in the box. I don't mean one foot in, I'm surprised the ref could even see Lukaku for the amount of players around him. Yet neither he, nor the assistant ref who's only job is to watch the goalie, noticed a thing.- meanonsunday