Michu looked to have put the home side on course for a third straight Group A win when he grabbed his sixth goal of the season, and fourth of this European campaign, by sliding the ball beyond Aleksandr Belenov in the 68th minute.
But the visitors snatched a point in stoppage time when Gerhard Tremmel brought down substitute Ibrahima Balde, and former Liverpool forward Djibril Cisse calmly scored from the spot.
The result means Swansea remain top of the group and move on to seven points, but it was a distinctly unimpressive display from the Welsh club against a limited opponent with just one win from their previous nine games.
And Valencia's romp to a comprehensive victory over St Gallen in Thursday's other group fixture moved the Spanish team into Swansea's wake on six points.
Laudrup felt a win against the Russian club on home turf would have given them one foot in the last 32.
He knows the task has become that bit more difficult as a result of dropping valuable points ahead of the 2,500-mile trip to Krasnodar in two weeks, although their destiny remains firmly in their own hands.
The Dane said: "We still have some more work to do. We have three very difficult games left, and two of them are away.
"With Kuban it will be difficult with the long hours travelling and the time difference, and then we face a completely different Valencia side from the one we beat in the Mestalla.
"The last game is a tough trip to St Gallen when the weather might be bad.
"We know your home games are very important in this competition, we beat the best team in the group away from home which changed everything, but we still have a home game to come and to have seven points at this stage is very good.
"We can still decide if we move on to the next stage."
But Laudrup had no complaints about the result, despite the equaliser arriving with just seconds left to play after Jonjo Shelvey had given the ball away in midfield
"When you are 1-0 up in injury time and they counter, get a penalty and an equaliser it is always disappointing," he said.
"But overall I think a draw is a fair result I have to say.
"We could say we should have kept the ball better at the end and not gone for the second goal, but we have to remember very few of our players have played in Europe, we are still learning.
"People think we should just beat teams from Switzerland and Russia, but these sides are difficult and competitive which has been shown many times."
Laudrup also refused to criticise Tremmel for conceding the spot-kick, having hesitated for a crucial split second before advancing off his line as Balde bore down on goal.
Laudrup said: "It's always difficult as a keeper, do you stand or go out?
"Gerhard is an experienced keeper, he is not 19 years old, and it is something we can't do anything about now, we have to learn from it."
Kuban boss Viktor Goncharenko, meanwhile, was delighted by his side's resilience as they picked up their first point of the campaign.
"We had nothing to lose so put a second attacker on late on and it worked," he said. "I was pleased with how we reacted to going behind and we defended well as a team.
"How you defend shows your attitude, but we still need to get better as an attacking side and I hope we can now pick up points in the Russian league, and we need to pick up points against Swansea and St Gallen in our upcoming Europa League matches."
Source: PA
Source: PA