The Swans have been in the top half of the table for most of the campaign but have struggled of late following their Capital One Cup success, winning just once in their last five outings.
In contrast, their opponents have pulled clear of the relegation zone and now lie 12th in the table, just three points behind ninth-placed City, to leave Laudrup concerned about their league position.
"We have six games to go and Saturday is a key game," he told the club's official website
"We have been in the top 10 for a number of weeks now and if we want to stay there we need a win on Saturday, particularly with the games we have after that.
"Beating the big teams is a bonus, but I'd prefer to beat the teams that are our direct rivals. I believe that if we win on Saturday then we will finish in the top 10."
Laudrup will test his mettle against Southampton boss Mauricio Pochettino once again when the clubs meet, with the two both having managed in Spain in the past, with Real Mallorca and Espanyol, respectively.
Former Argentina international Pochettino has all-but secured the Saints' Premier League survival for another season, masterminding victories over the likes of Manchester City, Liverpool and Chelsea and Laudrup praised his achievements.
"He did great at Espanyol as both a player and a manager," added Laudrup.
"When you go to a new country and a new culture, it is always difficult. But he is doing well at Southampton.
"They have done well recently after getting some important results against the big teams."
Meanwhile, Laudrup confirmed Wales international defender Neil Taylor is on his way back to fitness after injury having played for the U21 side against Millwall this week.
"He played 90 minutes on Monday and did well," said Laudrup. "It is great to see him back playing again after so long out.
"But I think we will see him before the end of the season, either in the team or in the squad. Whether that is this weekend, we'll wait and see."