The Swans are yet to pick up a win at the Liberty Stadium, with the only point coming from a 2-2 draw with Liverpool.
Laudrup's side fell to another defeat on Saturday, losing 2-1 to Arsenal.
Now, with Sunderland and West Ham United coming up, Laudrup wants to see his team pick up the home wins.
"It has been a tough start, Manchester United, Liverpool and Arsenal at home but that's how it is. We can't change that," Laudrup told reporters. "We have the same points now that we did at the same stage last year.
"Even if last year we had a fantastic start and then we had some losses, we have the same points. We have two games this week, a European game on Thursday and then we have to go to Southampton.
"After the break we start with two consecutive games at home to Sunderland and West Ham. Even if we won against Malmo and Ploiesti with 4-0 and 5-1 wins, of course we would like to return to win here in the league as well."
Swansea currently sit in 13th place after six games played.