The Swans scored five against Petrolul Ploiesti - with Wayne Routledge notching two - to put them in the driving seat to reach the Europa League group stages for the first time
The Welsh side were rampant at the Liberty Stadium on Thursday, as they effectively sealed their place in the group stages of the competition with a convincing first-leg victory.
Wayne Routledge scored twice in the first 25 minutes before Michu netted, while Wilfried Bony and Alejandro Pozuelo wrapped up the rout with further goals in the second half.
There was some late joy for the Romanians, as Gheorghe Grozav scored an outstanding overhead kick with three minutes left, but his goal could not take the smile away from Laudrup's face.
"In the first half we did well, scoring three goals, moving the ball around. They did not have one shot on target," the Dane told ITV.
"The second half I think we started well again and we scored a couple of goals. They scored one goal, a great one. I would have liked to have a clean sheet but if they had to score, I think that was an okay goal [to concede].
"But 5-1 overall, it is a magnificent result. I think we can look into the second leg with a lot of confidence.
"We want to go into that group stage and I think we did well today. We still have to finish like we did against Malmo [in the third qualifying round] after winning 4-0 here.
"But it's great to see. Four against Malmo, five today, it's good to see the boys scoring goals."
Swansea City captain Ashley Williams felt his side put in a "ruthless" performance but knows juggling domestic and continental commitments this season will be tough.
"It is obviously disappointing to concede a goal at the end. On the whole though, we were ruthless. That's what we want to do this season," Williams added.
"[Playing in Europe] is new for us. I imagine it is going to be tough and we are going to have to use more of the squad.
"It is tough playing on Thursday and Sunday but we have enjoyed playing in Europe so far."
The second leg of the fixture will be played in Romania next week.