Sunday's 3-1 defeat against Tottenham at the Liberty Stadium extended Swansea's winless run in the Barclays Premier League to eight games to leave them 15th in the table, three points above the relegation zone.
Emmanuel Adebayor grabbed a brace either side of a Chico Flores own goal to ensure Tim Sherwood remains unbeaten in the league since succeeding Andre Villas-Boas.
Wilfried Bony, whose fine individual performance was the highlight for Swansea, got a consolation for the hosts late on.
Swansea's injury list was also added to as Jonjo Shelvey's hamstring problem saw him join Michu, Michel Vorm, Pablo Hernandez, Nathan Dyer, Jonathan de Guzman, Jose Canas and Garry Monk on the sidelines.
The Welsh club's next league game is against 17th placed Fulham a week on Tuesday with fixtures against West Ham, Cardiff and Stoke following the meeting with the Cottagers.
Those four games could go a long way to defining Swansea's season, but Laudrup feels they are not far away from starting to move in the right direction up the table.
The Swans' manager said: "I knew that if we did not score when we were doing well in those first 25 minutes against Tottenham then what happened could happen.
"We need that little bit of luck and I hope we get it because we do not need much to turn things around.
"If we were playing poorly all the time it will be a lot more difficult, or if we have three players worried about having the ball it would be a much greater job - but I still think it is only about getting a win.
"There are a lot of teams in our situation in terms of points.
"We can go out now and win one or two games in the coming fixtures and things will change.
"Of course it will change the number of points and the position in the table, but it will give the whole team confidence because that is the only medicine and the next four games are important."
The win moved Tottenham up to fifth, level on points with fourth-placed Liverpool with the battle for Champions League qualification becoming ever-closer.
And Sherwood believes games between the top six with ultimately be crucial as he looks ahead to Spurs clash with Manchester City, who thrashed them 6-0 at the Etihad Stadium in November.
"It isn't easy, there are a lot of top teams up there and no-one is giving any leeway," he said. "I keep looking at results thinking sides might drop points and they don't. I'm sure a few thought we might drop points against Swansea.
"But we are not giving anything away either, so it will go down to the wire, it's about having consistency and belief and it will probably boil down to how we do amongst each other in that mini league.
"Our next game is Manchester City so we'll see what happens there, we could take a dent in our goal difference the way they are going, but maybe not.
"We don't see it like that, people may look at it like that as City are relentless at the moment, but we will try and impose ourselves on them as if you cower and keep on taking punches you get knocked out."