Liverpool appeared to assure themselves of a place in next month’s Kiev final with Mohamed Salah and Roberto Firmino braces coming either side of a Sadio Mané goal.
Yet Edin Dzeko’s 81st-minute strike and a Diego Perrotti penalty four minutes later offered handed Roma a lifeline for next week’s return leg at the Stadio Olimpico.
Eusebio di Francesco’s side still only have a slim chance of progressing but will take hope from their remarkable comeback against Barcelona in the last round, when they overturned a 4-1 deficit to go through on away goals.
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Klopp was delighted with what he saw from his players for the majority but Roma’s rally in the final 10 minutes left him feeling frustrated in the immediate aftermath.
“Long term perfect performance for pretty much 80 minutes or so,” Klopp told BT Sport after the final whistle.
“We made defensively one mistake. Penalty is not a penalty but that is the situation and now it is 5-2.
“Of course we would have been more happy with 5-0 or 5-1 but 5-2 is a fantastic result. We go there and try again.”
Klopp added: “We had all these runs behind, it changed the game completely and they couldn’t cope with that. We scored these goals and could have scored more.
“That is all positive, at this moment it doesn’t feel all positive because they scored these two goals but tomorrow I will see the really good part of the game.
“It is absolutely better than I thought before the game but at the moment of course a a little mistake.”
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