The city has spent the week in euphoric celebration following the Swans' emphatic 5-0 triumph over Bradford at Wembley. A victory parade was held through the streets on Tuesday, with thousands of fans lining the route, but Swansea must now return to Premier League action with the visit of Newcastle to the Liberty Stadium on Saturday.
Victory over the Magpies would see Laudrup's side reach 40 points, effectively securing Premier League safety and capping off an historic week in fine style. The Dane said: "There might be a negative reaction after winning the cup - I hope not - but it's a possibility."
He continued: "I hope the players go out and play the best game of the season, because this is the first game after the cup final, we are playing at home in front of our fans with the cup on display, so I hope - but I don't know.
"The fact we are now in the Europa League next season has nothing to do with our Premier League form, because we didn't start the season thinking about Europe. We have 37 points and we know with a few more we are safe.
"But we've been competitive all season apart from against Liverpool so we can't stop now. I still think we can at least arrive at 50 points and do better than last season, to get more than 46, and finish better than 11th.
"We are ninth and if we want to stay there we need 50 points, so that's 13 points from our last 11. That should be possible, but we have some very difficult games and we have to compete, otherwise we could lose most of them."
Since Swansea's glorious day at Wembley, there has been increased scrutiny on Laudrup's future at the club. Laudrup and chairman Huw Jenkins have stated the 48-year-old intends to honour his two-year contract.
Talks over a new deal have already started, although Rafael Benitez's precarious position at Chelsea will surely lead to further speculation Laudrup will end up at Stamford Bridge.
Laudrup said: "There is not much to say. I've said it a couple of times, my intention is to stay next season but, again, who knows about the future?"