Saturday's 2-1 FA Cup fourth-round win at Birmingham came at the end of a week when the training ground row between Chico Flores and Garry Monk had led to suggestions that all is not right in the Swansea dressing room.
A woeful first-half performance would have done little to dispel such concerns, with captain Ashley Williams not shy in letting some of his team-mates know they needed to raise their game.
But having battled back to claim the spoils thanks to Wilfried Bony's brace, Laudrup was at pains to stress his squad are united, and claims such stories would not be appearing were his side not on an eight-match winless run in the Barclays Premier League which has left them just three points above the drop zone.
"There is absolutely no problem with the harmony of the team," he said.
"This is what happens in football. There are so many cases and things always pop up when you are struggling.
"I don't want to use others as examples, but I remember last year there was so much talking about all the French players at Newcastle. This year they're exactly the same players - but I haven't read anything.
"All that has changed is they are playing good and they are winning, which is what football is about.
"On another level, look at all the stories that are coming out about Manchester United right now - last year, I didn't hear them.
"Last year it was Manchester City - again, this year I don't hear anything."
He added: "The bottom line is football is about results. When you are not there the media have to try and find a reason as to what is the negative influence on results.
"I played a lot of years and even in the good moments, sometimes you have two players who suddenly have go at each other in training. But it's not really an interesting story when you have just won six consecutive games, but it is when you have lost."
Swansea have yet to make any signings in January, but have been linked with moves for the likes of David Ngog, Rhys Williams, Anthony Pilkington, Tom Ince and Nathan Redmond.
But Laudrup is remaining tight-lipped on his plans.
"I won't comment on rumours and names," he said.
"I could do it every day, but the most important players are the ones here, even more so with the games coming up.
"If someone comes in he will be to help the squad. We will not sign Juan Mata, someone to come in and light up the whole thing.
"So if someone comes in it will to be a part of things here and not a star."