The Welsh club were on course for a crucial Europa League Group A win in Russia on Thursday thanks to Wilfried Bony's ninth-minute strike – his fifth in the competition this season.
However, despite the subsequent dismissal of Kuban defender Xandao, Ibrahima Balde snatched a 92nd-minute equaliser to prevent Swansea claiming three points.
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Kuban had also managed an injury-time leveller in the reverse fixture at the Liberty Stadium, but Laudrup was not downhearted after seeing his team's winless streak stretch to four games.
"In the first half, I think we played very good football. It was nice to see," Laudrup told ITV.
"We got in front, we had a couple of chances more. It was a very open game I think.
"Even at the end of the game, I think we did well keeping the ball. I understand the boys in there - they're disappointed – but, as I said to them, if we keep on going like this with the same spirit and playing the way we did in the first half, we will have no problems.
"In the first game we played them, you could say there were some mistakes (from us that led to Kuban's equaliser). Today - it was a great pass and a great finish. You can't say anything.
"We could have cleared the ball but I think it was a completely different performance to the first game we played against them."
Laudrup also felt his side were much improved from their 1-0 derby defeat to Cardiff on Sunday, and praised the efforts of Bony, who is set to shoulder additional responsibility with fellow forward Michu (ankle) facing a month-long lay-off.
"I think at Cardiff, we dominated quite well in the first half. We lacked in the last third," he said.
"Today we looked much sharper and there were some good performances. I feel sorry for the players because they deserve a win."