The Swans twice pounced on defensive errors from Branislav Ivanovic to net two precious away goals.
However, the Blues dominated much of the game leaving Laudrup feeling that the tie is still far from over and that his side must perform well in the return leg if they are to have a chance of lifting the trophy at Wembley:
“We’ve had some historic results already this season but to win at the European champions is very special, to be honest I’m delighted with the result.” He told Sky Sports.
“But there is still a mountain to climb. They have so much quality and we will have to play exactly the same; with the same intensity. They could still score three of four goals against us.
“But I am most happy about going into the second leg at home with a possibility to play a final at Wembley.”
Michu gave the visitors the lead with a precise finish in the first-half, after Ivanovic had failed to control a pass from goalkeeper Ross Turnbull.
The Serbian made another mistake with just minutes left to play, as Danny Graham, who came on for Michu, intercepted a sloppy back pass to round Turnbull and put the ball into an empty net.