The Ukrainians created a number of good chances at Old Trafford yet failed to find the net as David de Gea proved to be too great an obstacle.
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"Our failure to take our chances [in the first half] had a real impact on the game because we could have scored those goals but we lost - that's football," the Brazilian told Uefa's official website.
"We didn't expect the night to end like this but it's a lesson for us. We are learning and now we have to turn the page and try again next season.
"Now the Europa League: I think we've played in it once and won it [in 2009]. We will try to do that again. For us, and any other team, the Europa League is also important."
Shakhtar finished third in Group A with with eight points from six games, two points behind runners-up Leverkusen.