Facing a team with a world ranking four places below them, the 13th-ranked New Zealanders had hoped to do better than the last championship in Japan four years ago, when they bowed out at the same stage.
But a mixture of foul trouble to their leading players and solid rebounding by the taller Russians combined to deny them.
However, they will take pride from a three-match winning run - Lebanon 108-76, Canada 71-61 and France 82-70 - that put them in the knockout stages after suffering losses in their opening two matches to higher-ranked teams Lithuania 79-92, and Spain 84-101.
"It's disappointing not go through to the next round but I would not say it was a disappointing tournament for us," assistant coach Dillon Boucher said from Istanbul yesterday.
"To win one game at the championship is a big deal but to win three against the quality opposition that we were up against is an amazing achievement. We are definitely very proud of this team."
Russia's size ultimately wore down New Zealand as it broke clear in the third quarter with a 13-0 run.
New Zealand's hopes also foundered when star shooter Kirk Penney and defender Mika Vukona got into foul trouble, both with four to their name early in the second half.
Penney, whose tournament scoring average per game was 24.7 points, was well muzzled.
He was held to 13 points until midway during the last quarter before he added another eight points by which time it was too late.
Penney said Russia had done a good job milking the fouls while Abercrombie said the tough Russian defensive pattern had really hurt the Tall Blacks who had to do better to beat such teams.
"It's quite unsettling to the whole team when you can't be playing in the key stages of the game," Penney said.
"I'm not exactly sure what happened. I was called for numerous fouls early on and when you are sitting on the bench, you lose your rhythm and Mika went through the same thing. It was very frustrating. They made us play soft because every time you touched them there was a foul.
"We can't play that way. We are undersized and we need to play a physical game so it was incredibly frustrating to go out like that especially when you are sitting on the bench for much of the three quarters."
Coach Nenad Vucinic said he was not happy with the way the Tall Blacks had played.
"Offensively, things we usually do well we didn't do well.
"We really wanted this game so badly, we wanted it a little bit too much and we burned out.
"We wanted this win for Pero [Cameron] and Phill [Jones], who have retired from international basketball.
"They have been the stalwarts of New Zealand basketball, and without them we could not possibly have achieved what we have.
"We had three wins against tough opposition, and we are proud of what we have done."
Meanwhile, Chauncey Billups scored 19 points and Kevin Durant 17 as the United States powered into the quarterfinals with a 121-66 victory over Angola yesterday.
The Americans saved their most impressive performance in Istanbul for the knockout round, overwhelming the Angolans from the start after a couple of lacklustre performances to close the group stage.
Russia 78 (Andrey Vorontsevich 18, Tomofey Mozgov 16, Vitaliy Fridzon 12), New Zealand 56 (Kirk Penney 21, Thomas Abercrombie 13).
Halftime: 31-27.
