Stephen McManus headed into his own net and Bob McHugh missed a penalty as Kuban Krasnodar completed a comfortable 3-0 aggregate victory in the third qualifying round tie.
The Lanarkshire side were relatively comfortable, without having seriously threatened to cut their 2-0 first-leg deficit, before McManus diverted the ball into his own net five minutes into the second half.
Motherwell, who were without three key attacking players, had the perfect chance to level in the final minute after Djibril Cisse handled Stevie Hammell's free-kick but substitute McHugh saw his effort saved.
Their small band of fans at least had something to celebrate earlier when Gunnar Nielsen marked his debut with a 75th-minute penalty save from Charles Kabore.
With a six-and-a-half-hour flight after the game, Motherwell manager Stuart McCall took the bold decision to leave key attacking players James McFadden, John Sutton and Iain Vigurs in Scotland to prevent them aggravating muscle issues ahead of Sunday's Scottish Premiership clash with Aberdeen.
Despite the absentees, Motherwell made a steady start with chances few and far between for the hosts, who have not been beaten in the Russian Premier League since November last year.
Motherwell almost got in behind the hosts twice with Francis-Angol threatening to break clear until he was caught up, before Anier's driven cross was deflected just wide after he pounced on a short header back.
Ibrahima Balde almost got through on goal three times from Kabore balls but Motherwell survived each time and Nielsen made his first save in the 36th minute when he got down to hold Balde's long-range strike.
But Motherwell's first-half resistance was ruined by McManus's misjudgement when left-back Roman Bugaev sent over a cross into the six-yard box and McManus headed straight into the top corner as he tried to clear over the bar.
Nielsen soon produced an excellent one-handed save to push away a 25-yard strike by Marcos Urena and then held Balde's curling effort as the hosts stepped up a gear.
But Motherwell threatened when Kerr got round the outside following Paul Lawson's diagonal ball and crossed for Anier, who turned his man but was closed down as he shot, before Keith Lasley saw his follow-up shot charged down.
Nielsen got his chance to shine when Hutchinson caught Balde after some quick feet from the Senegal striker. Kabore hit the penalty low and hard to the right of Nielsen but the Faroe Islands international got down quickly and produced a strong hand to push the ball away.
Motherwell then looked set to end their European adventure on a further high but Aleksandr Belenov dived to his left to push away McHugh's powerful spot-kick to make it seven consecutive European games without a goal for the Steelmen.