The Swans were all but assured of progression after their 4-0 win at the Liberty Stadium last week, and they were rarely troubled at the Swedbank Stadion.
At the other end another clean sheet was racked up, meaning Swansea have conceded just one goal in their build-up to the new Barclays Premier League season.
"I am satisfied overall," said Laudrup, who made seven changes from the first leg. "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.
"If we want to find something negative, we did not play that well offensively. 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.
"I am very happy with that. Next week it's Manchester United in the Premier League, but when you have that confidence it is important for the whole team, not just goalkeepers and defenders."
Laudrup also expressed his admiration for defender Chico Flores on his return from injury.
The Spaniard's father died last week but he turned in a tremendous performance alongside Ashley Williams at the heart of the Swansea defence.
Laudrup said: "He has had a hard time, especially off the pitch with things in his private life and he has been injured too.
"He has shown character to quickly move on and it is good to have him back."
Swansea will discover their play-off opponents at midday on Friday, but their results in other ties mean they will be seeded and Laudrup hopes they will again avoid any arduous away journeys.
He said: "We will be seeded so that is good and means we avoid some of the big teams in there, although there are good teams in the other half (of the draw).
"There are some Swedish, Danish and Norwegian teams and some Eastern European sides as well.
"I hope we will have a good short trip, this has been perfect, but I would like to play away in the first leg."