With Premier League survival the main priority, Laudrup knows the trip to face the bottom-of-the-league Royals, who have suffered seven straight defeats, is arguably more important in terms of ensuring Swansea remain a top-flight club.
He said: "The result against United was a great result for the club, the players, the staff and the supporters. We can enjoy it for 24 hours or so but from Tuesday we have to start thinking about Reading as it is even more important. It is a key game."
He added: "It is our last game in the first half of the season, and if we win that it would be fantastic. In fact for us to turn around with 27 points would be excellent."
Teenage left-back Ben Davies admits the Swans are brimming with confidence after taking a point off United, but are taking nothing for granted despite Reading's struggles.
"We have a lot of confidence going into that game against Reading after a big draw and a big performance," he said.
"We have every right to go there and try to get three points.
"Hopefully we can do that if we match our last performance.
"We can't go into it expecting an easy game from them because they're fighting for their lives, and I don't think we will get an easy game.
"We've got to go into it looking to get three points and it will be a big three points if we can get them."
Source: PA
Source: PA