Motherwell boss Stuart McCall commended his players for their battling performance despite
A Stephen McManus own goal separated the two sides in the second leg with Kuban going through to the playoff round 3-0 on aggregate.
Both teams had penalties saved, but McCall was disappointed that the Steelmen's efforts were not rewarded.
"The penalty would have been the icing on the cake," he told BBC Scotland.
"Other than when we gave the ball away once or twice, they didn't open us up."
Ibrahima Balde continued where he left off from the first leg, causing the Motherwell defence problems with his ingenuity and guile on the ball.
Charles Kabore, who missed a spot-kick for the hosts after Shaun Hutchison brought down Balde, was also lively in midfield and the Well boss concedes they were up against tricky opponents.
"I've watched them four times now and they are a really good side," he added.
"The boy up front, Balde, they're talking £10m, the boy in the middle of the park, £8m. They've got quality running through the side.
"I'm pleased we pushed them as close as we did. Mick [McManus] is disappointed with the own goal, but that happens in football and Gunnar [Nielsen] made a penalty save.
"We didn't create a great number of chances but I thought we limited a good side to long-range efforts.
"I was really pleased with them and it would have been justice for our efforts over the two legs if we had scored that penalty at the end."
McCall would have been happy with the first-half display, as they fashioned a couple of chances through Estonian forward Henri Anier and Zaine Francis-Angol.
He added: "If we had got the draw, I think we might have just about merited it.
"We wanted to get to the 60-minute mark without conceding and then we would have frustrated them. We could have grabbed a goal at the other end which could have changed the tie.
"But we lost a goal early in the second half. A lot of teams could have crumbled, but we never. We stood up and got back into the game, putting in a great deal of effort.
"Sometimes you score own goals, you don't want it to happen, but McManus led the team really well at the back."