The Welsh outfit have yet to register a home success in the top flight this season, with a 2-2 draw against Liverpool the only point claimed by the side at the Liberty Stadium.
Their latest setback on home soil came in Saturday's 2-1 defeat to Arsenal, as a first professional goal from Serge Gnabry and an Aaron Ramsey strike put Arsene Wenger's charges into a commanding position.
Full-back Ben Davies notched a late consolation for Swansea, but they did not have time to force an equaliser.
Swansea face a trip to Southampton in their next Premier League outing, but host Sunderland and West Ham at the Liberty after the international break.
The club have tasted success at in their own back yard this season, with big wins against Malmo and Petrolul Ploiesti in the UEFA Europa League.
But Laudrup is keen to take their European form into the domestic campaign and start picking up maximum hauls in their league fixtures.
"It has been a tough start," he said. "Manchester United, Liverpool and Arsenal at home but that's how it is. We can't change that.
"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 (international) 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 (in the Europa League), of course we would like to return to win here in the league as well."
