The Swansea boss had pinpointed before Sunday's game at the Cardiff City Stadium that his opponents' main threat was from set-pieces.
So it proved as Steven Caulker headed home Craig Bellamy's corner in the 62nd minute to settle a game of few chances.
"It was a very tight game, we knew it was going to be that, and they scored from a set-piece," Laudrup told Sky Sports.
"We know they score goals from set-pieces, and from one corner they scored a goal, which was more or less what they had in terms of chances in the whole game.
"That's how football is and we have to accept it, even if it hurts. Of course, it hurts to lose a derby, but that's how it is.
"We knew in general that they are strong at set-pieces, like some other teams as well, and they scored some important goals in early matches in the season.
"I think in the first half they had three or four, and you can't keep them away from having any corners at all. They had five or six, and the one they scored from wasn't really a chance."
Swansea finished the game with 10 men after goalkeeper Michel Vorm was sent off in stoppage-time for bringing down Fraizer Campbell as the Cardiff striker bore down on goal.
Laudrup accepted the decision of referee Mike Dean, saying: "He's the last man, it's what can happen."