Laudrup's side secured a comfortable 4-0 win over Malmo on Thursday night in the first leg of their Europa League third qualifying round tie.
Michu opened the scoring in the first half before two goals from record signing Wilfried Bony and a goal from fellow debutant Alejandro Pozuelo sealed the win.
New United manager David Moyes was in the crowd to watch them as he prepares to bring his side to south Wales for Sunday's Sky Live game and his opposite number is convinced Swansea will be well prepared for them.
"It's great to play these two serious games before the league starts," Laudrup said of the two games with Swedish side Malmo, which come either side of the clash with United.
"It's great for us to play a very important competition rather than two friendlies. I was happy to start now because of this.
"We can use these games as preparation for the Premier League.
"We know cup competitions are important but the Premier League is our daily bread. It is where we want to be and it is where we want to consolidate ourselves as a squad and a club this season.
"The players know what we want to do, but for now we just have to think about the one game we have played.
"We have conceded only one goal in pre-season - that gives confidence to the team - and we have looked strong at set-pieces.
"That was one of our weak points last season and it looks like we are improving there."