The hosts only named Robin van Persie on the bench for the match, but fellow Manchester United alumnus Nani almost gave them a perfect start when he tested Andriy Pyatov with a 20-yard effort just five minutes in.
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Shakhtar soon gained a foothold, however, and spurned the best chance of the half 10 minutes later when Alex Teixeira put the ball inches wide of the target when unmarked in the area.
Nani turned provider late in the half with a lofted ball forward to Fernandao, but his header was too high as the opening 45 minutes ended goalless.
The second half did not provide quite as many chances, but the majority that did arrive fell to Shakhtar and Taison in particular.
Ten minutes into the half the Brazilian danced past a number of challenges on his way into the box, only to put his eventual effort wide. Then, shortly after the hour mark, he produced a snap shot from the edge of the area that beat the keeper, but also went the wrong side of the upright.
The hosts were struggling to really assert themselves in the final third and were mostly limited to long-range efforts, the best of which saw Diego flash one past the post from around 25 yards.
There was a competitive debut for Van Persie with a little over 20 minutes remaining, but the Dutch striker was unable to make a difference as both sides were forced to settle for a draw.