Wilfried Bony opened the scoring for the visitors, before Krasnodar were reduced to 10 men following the sending-off of Xandao.
However, in the final minute at the Kuban Stadium, Ibrahima Balde forced home an equaliser to deny the Welsh club in their fourth Europa League match of Group A.
It was a similar story at the Liberty Stadium last month when Krasnodar netted a late goal in another 1-1 draw.
Yet manager Laudrup was not too unhappy with his players, admitting they performed well following their defeat to rivals Cardiff at the weekend.
The Dane said: "They scored in injury-time like last time but when you look overall the two games were completely different.
"We were very pleased to see the reaction and the performance in the first half.
"We played some good football and there were good individual performances.
"We had good chances and went in front and it was quite an open game. I thought we did well.
"In the second half we tried to play a little more on the counter and had chances but the goal came.
"It was a ball we had to clear but it was a good pass and a great finish.
"In the end we learned from the first game and we kept the ball so we cannot say anything about that.
"I feel sorry for the players because I think they deserved to win this game.
But sometimes you need a little luck.
"Whatever happens, if we win the next game we are through, we know that.
"It's always positive if you can decide your own fate and we can do that. In the next round of games, whatever happens, it is down to us."