Swansea maintained their impressive record against the Barclays Premier League's big guns as they secured a 1-1 draw against United on Sunday, Michu's 13th league goal of the season cancelling out Patrice Evra's opener at the Liberty Stadium.
Swansea had previously taken points off Arsenal, Chelsea, Liverpool and Newcastle this term and sit 11th in the table having amassed 24 points from 18 games.
But with Premier League survival the main priority, Laudrup knows the trip to face bottom club Reading, 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.
"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."
Laudrup may decide to make changes against the Royals given the quick turnaround from the meeting with United.
The Dane hopes to have Pablo Hernandez available after almost four weeks out with a thigh injury, but full-back Angel Rangel is unlikely to be risked as he looks to recover from a calf problem.
Laudrup said: "Both Pablo and Angel have muscle injuries and you have to be careful with muscle injuries as if you start too soon you can lose them for three weeks, which could mean six or seven games for us.
"He will be with us when he is ready, that could be against Reading, with Angel he might be back for the Fulham game."