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The Giallorossi took the lead at the Metalist Stadion through Cengiz Under, but ultimately succumbed to second half strikes from Facundo Ferreyra and Fred.
The result means Eusebio Di Francesco’s side will have to win at the Stadio Olimpico if they want to reach the quarter-finals.
“We got the opener and were almost perfect in the first half,” Alisson said. “We didn't fall apart but we did drop off a bit.
“We struggled to deal with it but this game's in the past now and we have to look forward. In the end it came down to the small details.”
The Brazilian goalkeeper made a number of eye-catching saves during the match.
“When you give a team like Shakhtar space to play in they're very good on the ball,” he added. “They have quality players at both ends of the pitch.
“On that last chance it was Bruno Peres who got the vital touch – he did brilliantly. He came on in a very tough match and did well after not playing for a while.
“2-1 is not the result we were hoping for but we're still in it. Now we must turn our attentions back to our domestic commitments."
Imperium Partners
Centurion Partners
