The reverse fixture in Swansea had ended with the same scoreline after Djibril Cisse's last-gasp penalty, and the Swans were again undone in injury-time at Kuban Stadium as Ibrahima Balde cancelled out Wilfried Bony's opener for the hosts, who had defender Xandao sent off with 15 minutes remaining.
The result means Swansea have now won just twice in their past nine games in all competitions, and must wait for the chance to secure progress from Group A, which would have been confirmed with a victory in Russia.
However, Laudrup was pleased with the response from his players after Sunday's derby defeat to Cardiff, but just felt they had lacked a bit of good fortune.
"They scored in injury-time like last time but when you look overall the games were completely different," said the Dane.
"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."
One positive for Swansea was the performance of Bony, who finished emphatically in the ninth minute after excellent work from Alejandro Pozuelo and Roland Lamah, making just his third start for the club.
Laudrup has used his B£12million record signing sparingly since his summer arrival from Vitesse Arnhem and recently claimed the Ivorian is not up to speed in terms of his fitness and adaptation to English football.
But with talisman Michu sidelined by an ankle problem, Bony put in a performance that suggested he is ready to shoulder the goalscoring burden.
Laudrup said: "There were positives for every forward, but it was important for him to score a goal.
"He had a chance to come in, he was very active and involved in a lot of good movements.
"He got a little tired but that's okay for me because it is important we get the best out of him and it was a big step in the right direction, so I m happy for him as he scored a goal and goals are so important for forwards."
Having produced a strong first-half display Swansea faded as the second half went on, cheaply losing possession and inviting Kuban on to them.
Matters were not helped when Laudrup substituted Bony, Lamah and Nathan Dyer - three of Swansea's best performers on the night - but Laudrup defended the decision.
"Roland has not been playing a lot so it's normal. He gave a lot, he was fantastic in the first 45 minutes and it's normal after an hour he would be tired," said Laudrup.
"Nathan is one of the players that has played the most this season and at that time I thought too many times we ended up with four up front and too much work for our two midfielders, so I wanted to strengthen that area."
Despite that setback, and seeing Valencia go top of Group A with victory over St Gallen, a win from either of their two remaining games will see them go through to the last 32.
"Whatever happens, if we win the next game we are through, we know that," said Laudrup. "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."
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- Wilfried Bony