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."