Goals from Dan Burn, Matt Green and Tom Adeyemi gave the Championship club a superb victory at St Andrews but Swans boss Laudrup felt it could have been a completely different story if his players had taken their chances.
"I don't think I'm wrong if I say we could have been four up at half-time," Laudrup told Sky Sports.
"And then with Birmingham's first chance they score, and then the other two goals I think there was a little misunderstanding at the back and in the end we lost the game.
"If you have to be positive then we create a lot of chances in every game but, yes, you have to score otherwise this can happen.
"I think in the first half Birmingham did not even have one chance, a couple of shots on target, nothing more.
"We could have scored at least four but we didn't and then it gives them the confidence and belief that they can come back into the game and they did."