Roma were subsequently able to see the game out for an aggregate score of 2-2, which saw them through to the quarter-finals thanks to Under's away goal in the first leg.
"Roma started the season well, there was a period when things weren't going at their best and we could've done better in Serie A, but I feel we've had this black-out in every season and need to improve that".
Shakhtar's chances of producing a comeback were dealt a huge blow in the 79 minute when they were reduced to 10 men following the sending off of Ivan Ordets after straight red card.
Alessandro Florenzi flicked a risky backwards header just wide of his own goal and a nervous home crowd witnessed the visitors maintaining a level of control throughout the first half, Pyatov intercepting when Aleksandar Kolarov led a rare Roma foray. Then, Shakhtar's Ordets fouled on Džeko and was sent off.
"A fantastic result, a fantastic Roma: among the best eight sides in Europe", he posted.
Goal scorer Dzeko had no doubts, saying Roma were "deservedly" through, and he said the chance to move on with Roma was a big reason why he stayed on in January, despite interest from Chelsea.
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But he warned that the border between Northern Ireland and the Republic could be a major roadblock to sealing a deal. He said it "translates faithfully" the agreement reached between Theresa May and the European Union in December.
Mallenco twice worked for the matches of Shakhtar in the Champions League in the 2014-2015 season, "miners" in the 1/8 finals of painted draw with Bayern (0:0), and in the autumn of previous year thanks to the double beat Bernard "Feyenoord" (2:1). "If we face any opponent with this attitude and determination, then we can go far".
- This is the first time Roma have progressed from a knockout tie in which they have lost the first leg; ending a run of five consecutive knockout tie defeats.
- Shakhtar Donetsk failed to register a single shot on target against Roma in this match.
Roma held on, and after Italy's shock failure to qualify for the World Cup, their progress to the last eight along with Juventus is a boost for the country. In the group stage of 2007-2008 Champions League, the Spaniard recorded the Shakhtar's win over Benfica (2:0).
There will also be at least three Italian coaches in the quarter-finals - Di Francesco, Massimiliano Allegri of Juventus and Vincenzo Montella of Sevilla.