Swansea secured their first win at the home of Manchester United last weekend with a 2-1 victory in the third round of the FA Cup.
Earlier in the season Everton had recorded a first win there in 21 years, while Newcastle's success was a first in 41 years.
Tuesday's defeat to Sunderland in the semi-final of the Capital One Cup marked the first time United have lost three games in a row since 2001, and a further loss to Swansea would make this the Red Devils worst run since 1961.
But the Dane is more concerned about picking up an important three points for his side.
"For me it's just statistics, it doesn't mean anything," he said. "I am happy to be the first manager at this club to win at Old Trafford, that is one thing, or to win a trophy like the League Cup last year, they are statistics I like.
"To be part of a team that gives another side a bad statistic, I don't really care."
Laudrup also admitted he has sympathy for Moyes as the Scot struggles with the task of succeeding the patriarchal figure of Sir Alex Ferguson.
"Of course, I have sympathy for all my peers," he said.
"I also have sympathy for Sam Allardyce, who didn't look too happy the other night, because I can put myself in that exact same position and know what he's feeling.
"You can take it one by one, even the ones who are happy like Manuel Pellegrini and Arsene Wenger.
"They are colleagues and you are in a very special position as a manager because you are the one.
"There are staff and players but a lot of times you are alone with your thoughts and what you have to do and it's just you who has to make the decisions.
"It is you people pick on when results are not there. When things are good it's you and the players, when things go wrong it's just you, because it's easier to pick on one than 15 and it's easier to change one than 15.
"So of course I can relate to all the good and bad things my colleagues are going through."
Swansea's hopes of another success will not be helped by an extensive injury list.
Laudrup will be without Michel Vorm, Michu, Dwight Tiendalli, Nathan Dyer, Jonathan de Guzman, Pablo Hernandez and Roland Lamah for the second trip to Old Trafford in a week.
But the Swans boss is hopeful that at least some of those players will be back for the meeting with Tottenham in just over a week.
He said: "I think Michel will be back for Tottenham or for the FA Cup game the week after.
"Dwight could be back, Jonathan could be back, we well as Lamah, Dyer and Pablo. They are all in contention for the Tottenham game.
"Maybe we will have three back or four back, but it is only Michu who is out longer. He will be back in the first or second week of February."