Laudrup arrived at the Liberty Stadium in the summer with a reputation for producing sides who played attractive, attacking football and scored plenty of goals, but were also liable to concede at the other end.
The Swans are unquestionably a greater attacking threat this term, mainly thanks to the goalscoring heroics of Michu, but their excellent run of just two defeats in 17 games has been based upon a solid defensive foundation.
Ashley Williams, Chico Flores and young Ben Davies have excelled as part of the back four, with Angel Rangel, Garry Monk and Dwight Tiendalli also making notable contributions.
Such has been the level of performance, Swansea have conceded just 11 goals in nine games away from home in the league this season, which along with Arsenal is the joint-lowest total in the top flight.
Having triumphed 2-0 at the Emirates Stadium earlier this season, Laudrup knows more of the defending seen on that occasion, and in keeping clean sheets at Chelsea and Everton, will be required on Wednesday night to secure safe passage through to an FA Cup fourth-round meeting at Brighton.
He said: "We have shown throughout the season, but particularly in the last two games, how solid we are. I have even been a bit surprised by how solid we have looked defending deep.
"I always try to say not to defend so deep. Against Chelsea, it is one thing as they don't play many balls into the box, but Everton do with a lot of big guys up there and we did great and and that is really good to see.
"In 11 away games we have only conceded nine goals which is quite good for a manager who always played up front.
"But the players know if they are a little relaxed against the big teams you can get hurt really bad."
Wednesday night's third-round replay has added to an already hectic month for the Swans, with the Capital One Cup semi-final with Chelsea also increasing their workload.
But Laudrup is adamant the congestion does not put the FA Cup at the bottom of his list of priorities.
He said: "The 11 or 14 who play will do everything to win and Arsenal are the same.
"I cannot tell the players who go out 'just play at 50 per cent because we don't really care about winning this game', you cannot do that.
"In the first game in this tie, we were up and then we were down.
"We could have won the game and lost the game but we fought and got a draw in the end and it shows that the 11 who go on the pitch will give their all."