The Welsh side will face Petrolul Ploiesti in the play-offs for a place in the group stage after comfortably beating Malmo 4-0 on aggregate in the third qualifying round
Progression in the Europa League came after a 0-0 draw in Malmo on Thursday saw them comfortably through following a 4-0 first-leg victory at home last week.
It marks the first time back in European competition for the Welsh outfit since the 1991-92 Cup Winners' Cup, and Laudrup feels that Swansea's strong backline is to credit for the achievement.
"I am satisfied overall," he said. "We are through to the next round. We knew we were almost there and I think it was a professional performance.
"They had a good chance in the opening moments but we dominated the game and had good opportunities.
"From these two games we have two clean sheets and have not given our opponent many chances."
It also means that Laudrup's team have conceded just one goal in the lead-up to the new Premier League season, which begins for them against champions Manchester United on August 17.
Laudrup is now keen to see his side attack more in their next European encounter, with the draw for the play-off round due to be announced on Friday.
"If we want to find something negative, we did not play that well offensively," he added.
"We have to do much better in that area but when you play away you can't always dominate and clean sheets are very important."