Swansea are top of Europa League Group A after victories over Valencia and St Gallen, while Kuban are bottom of the pile after losing to the same opponents.
A third successive win on Thursday would put the Swans on the verge of the knockout stage but Laudrup remembers the time his European Cup-winning Barcelona team were dumped out of the following season's competition by CSKA Moscow and no-one ightly.
"I remember it well, because in May 1992 I won the Champions League at Wembley with Barcelona against Sampdoria," the Dane said. "Just after that, the following November, we had to play a play-off before going into the group stage.
"We played CSKA and drew 1-1 away. Then we were 2-0 up after 30 minutes of the home leg and everybody thought it was done, but we lost 3-2.
"It was a big surprise, and it could be an example for us because even though it was 2-0 after 30 minutes it showed you have to be 100 per cent focused.
"We had a fantastic team, better than CSKA with all respect, but they went on to the next round, we can use that tomorrow."
With away trips to Russia and Switzerland still to come, and a rejuvenated
Valencia yet to visit the Liberty Stadium, Laudrup knows just how important victory on Thursday could be as Swansea look to extend their European campaign beyond Christmas.
He added: "We're at home, we'll be favourites and we're top of the group and want to win for a lot of reasons.
"The first is that getting to nine points will give us one foot, maybe one and a half feet, in the knockout stage.
"After this game we have two difficult away games. We go to Russia with all the travelling and the time difference, and then Switzerland where there will be cold weather. We also have Valencia at home so this is a key game for us.
"I think 10 points should be enough to get us through, but we might need