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Anzhi had some early spells of possession, but were unable to make any real impact in the final third. Oleksandr Aliev attempted a long-range effort at goal for the home side, but it flew well wide of the target.
Minutes later, Nemanja Gudelj came close for the away side once again when his free kick shot smashed against the left post, leaving the scoreline goalless.
After the break, Anzhi went on the front foot, but at the other end, Johannsson came close again when he launched a shot on the edge of the penalty area, but Kerzhakov was able to make another save in the top left corner.
Kerzhakov came to the rescue once again by stopping Steven Berghuis's effort from the edge of the box, but the AZ player had another chance to break the deadlock minutes later. He managed to drive inside the box, but failed to get the shot on target.
The home side tried a late surge in the second half in a bid to keep their place in the tournament, but despite some efforts from Serder Serderov and Aliev, the Russian side succumbed to a 1-0 aggregate defeat.