A 0-0 draw with Southampton at the Liberty Stadium on Saturday meant the Capital One Cup winners have now gone five games without winning in a slumping end to their campaign.
They stay in ninth position but, with difficult games against Chelsea, Manchester City and Manchester United in their remaining five fixtures, there is a risk of being overtaken.
Tenth-placed West Ham United sit level on 42 points while Fulham are just two points behind and Southampton trail by one additional point, leaving Laudrup a little concerned.
The Dane, who had described the Southampton game as must-win, told Sky Sports: "It means we will have to get the points elsewhere. I do not know how many points we will need to stay up there.
"But West Ham won. At least we keep Southampton three points behind. I think we need four to six points.
"We have to find them somewhere and of course it will not be easy with some of the games coming up. But that is life."