Laudrup's men have not won in their last six Premier League matches and sit four points above the drop zone in 13th.
Ahead of clashes with champions Manchester United and in-form Tottenham Hotspur, Laudrup feels the confidence within his squad is a promising sign.
"As I long as I can see that there's a lot of confidence in the team… then I'm not worried," the BBC quotes him as saying.
"I have a lot of respect for the numbers and it could be moments when we are just a few points away from that bottom three."
After the visit of Tim Sherwood's men on January 19, Swansea's next three opponents, Fulham, West Ham and Cardiff City, are all side that occupy spots in the bottom five.
Laudrup believes if his side are to boost their survival hopes, results against those around them are essential.
"We just have to pick up points and especially when we (face teams in the bottom half)," he added.
"We know there are some difficult games coming up but if we do play as we have done in recent games we will pick up the points."
