The city has spent the week in euphoric celebration following the Swans' emphatic 5-0 triumph over Bradford in the Capital One Cup final at Wembley.
A victory parade was held through the streets on Tuesday, with thousands of fans lining the route, but Swansea must now focus on 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.
But the Dane wants his side to show their maturity and push on to secure a higher tally than the 46 achieved under Brendan Rodgers last season.
He said: "There might be a negative reaction after winning the cup - I hope not - but it's a possibility.
"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?
"That is the only way I can answer and the same next week and next month, so I want to leave it there and go back to what is important which is the games.
"I've never said I do not want to manage a big team one day, it is just not a dream of mine - that's different.
"If I go somewhere one day I do, if I don't I don't. It has nothing to do with ambitions, I have ambitions - how can I not after playing at big clubs for 17 years and winning titles?
"I just don't have a plan for three years' time. It's just how I feel."
Laudrup also confirmed defender Chico Flores is still a few weeks away from making a return after rupturing ankle ligaments, but left-back Neil Taylor is back in training after six months out with a broken leg.