Swansea stunned the Spanish club and claimed one of the most famous wins in their history when they secured a 3-0 victory at the Mestalla in the opening round of Group A fixtures.
The win came during a miserable start to the season for Los Che and heaped pressure on coach Miroslav Djukic.
Their form initially recovered, and three consecutive Europa League wins mean they have already reached the knockout stages and sit top of Group A.
However, they have lost four of their last six games in the Primera Division and lie 11th in the table.
The club have also recently appointed a new sporting director to work with Djukic, although Francisco Rufete has not made the trip to Wales.
But, despite recent form, Swans boss Laudrup believes the freedom of having already nailed down a place in the last 32 will mean it is a very different Valencia team come Thursday evening.
He said: "When we played them at the Mestalla, it was under special circumstances. They had come off the back of three defeats in the league.
"Obviously it was special for this club to beat one of the big teams in Spain, people here could tell you that.
"But then they came back on track, they won a few games.
"They have lost a few in the last few weeks, but it will be different to the game there because they already qualified, they don't have to think about this competition before February so it changes things.
"It was a great win because of the reputation of Valencia.
"They have played in the Champions League and reached two finals last 12 years ago.
"We played a great game out there, but we have to remember they played 80 minutes with one man less (after Adil Rami's red card) and in difficult circumstances because of the atmosphere.
"We played well, it was a good game, and it would be nice to repeat. it but it won't be easy.
He added: ""I have watched them a lot lately because of this game including the match with Elche at the weekend and I thought they played very well in first half.
"But they lost the game and this happens in football. It's difficult because sometimes nothing seems to go your way, it's normal and it's happened to us here.
"We are still facing one of Europe's big teams. You can't change a history of a club for a couple of mediocre seasons; it takes many years to write a history of club, although they are now playing in the Europa League after being Champions League finalists, we should not doubt the big history this club has had."
Swansea would themselves have secured qualification from the group had they managed to hold on for victory in either of their two games against Russian club Kuban Krasnodar.
But conceding stoppage-time equalisers in both fixtures mean Swansea still have work to do.
A win would guarantee their advancement, while a point may prove to be enough depending on the result in Kuban's clash with St Gallen.
Laudrup insists Swansea's recent run of conceding late goals, with a potential Premier League win over Stoke also being relinquished in added time, is firmly behind them after the weekend victory over Fulham.
He said: "All the players were disappointed it happened, it happened in the Premier League too.
"So you don't have to talk about it because sometimes the more you talk when about it the more you feel it.
"You could feel it against Fulham at the end, but now we're past it we don't have to talk about it."
Laudrup hopes to have winger Pablo Hernandez back against his former club. Hernandez has played just 29 minutes since September 1 due to a thigh injury which flared up again after his initial recovery.
"Pablo is a possibility for this game," said Laudrup.
"I don't think he's desperate to play against Valencia, he is desperate just to play. He was out for many weeks, he came back for half an hour and then he was out again.
"He has a lot of desire to play. He has looked quite good in training but a game is another thing."