Swansea sit top of 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 sealing a place in the last 32, and they are fancied to do so with their visitors having failed to register a win in their last nine games.
But Laudrup knows from his own playing career - namely when his European Cup-winning Barcelona team were dumped out of the following season's competition by CSKA Moscow - not to take Russian opposition lightly.
The Dane said: "I remember it well, because in May 1992 I won the Champions League at Wembley with Barcelona against Sampdoria.
"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 does not hurt so much now as I had won the competition a few months earlier.
"But 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."
With away trips to Russia and Switzerland still to come, and a rejuvenated Valencia yet to visit the Liberty Stadium, Laudrup understands just how important victory on Thursday could be as Swansea look to continue their European campaign beyond Christmas.
He said: "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 11."
Laudrup is again without captain Ashley Williams as the defender's ankle ligament problem continues to keep him sidelined, while left-back Ben Davies will be out until after November's international break with an ankle sprain.
But the Dane is confident in the abilities of Jordi Amat and Neil Taylor, who missed almost all of last season after breaking his ankle, to deputise.
He said: "Unfortunately people get injured and no one knows that better than Neil," said Laudrup.
"But it's part of football and I always try to use the squad because suddenly you will need player for four or five consecutive games for reasons like this.
"Jordi is the same. Neil was unlucky after coming back from a long period out, he played a few games and then had another, smaller injury which was a setback.
"But he has come back and played a couple of games with Wales and came on against Sunderland and it's good for him because he now has a little more match fitness."
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