The Canaries had stunned their high-flying hosts with goals from Steven Whittaker, Sebastien Bassong and Grant Holt giving them a 3-0 half-time lead.
Swansea rallied through strikes from Michu and Jonathan De Guzman but Robert Snodgrass made sure of the win with his excellent free-kick before Michu netted again in stoppage time.
Laudrup said: "We did not play well in the first half. We were 3-0 down and obviously we came out and had a great reaction in the second half.
"We scored two and it could have been three but we had an equaliser disallowed.
"But overall we did not deserve it after the first half. I knew there would be reaction one day after all the positive things people have been saying about us.
"I did not know when it would come but it came in the first half."
- Sports & Recreation
- Sebastien Bassong
- Jonathan De Guzman
- Robert Snodgrass
- Steven Whittaker