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Mohamed Salah's early penalty in Bergamo gave Liverpool hope that it could turn around the 3-0 deficit from the first leg.
But Atalanta held firm and didn't concede any further goals.
With six games left, time is running out and no further points can be dropped at this stage.
READ MORE: Liverpool might have quiet title hope thanks to Champions League change and new Spurs reality
READ MORE: Liverpool 'has spoken to surprise new manager option' as three stars to follow Jürgen Klopp out
In the background, the club is yet to appoint a new manager, but Sporting CP coach Rúben Amorim is the hot favorite to succeed Klopp.
There are also links with a move away for a current Liverpool midfielder potentially leaving the club.
Viktor Gyökeres (Sporting CP)
According to Portuguese outlet Correio da Manha (print edition via Paisley Gates), should Rúben Amorim arrive at Liverpool this summer, he could attempt to take star striker Viktor Gyökeres with him.
That seems unlikely, though, so bringing in another number nine would be an odd move.
Liverpool.com says: Gyökeres' record this season is extraordinary, but having bought Darwin Nunez two years ago from Benfica, and given all of his trials and tribulations since, Liverpool may refrain from buying a striker from Portugal a second time.
Ryan Gravenberch (Liverpool)
The Dutchman was signed in the final days of the summer transfer window, but has struggled to make an impression in his first season in England after arriving from Bayern Munich
Gravenberch has, to date, made 33 appearances for Liverpool in all competitions, but only 19 of them have come as a starter.
Lately, he's been an unused substitute in the last four consecutive games, and a report from Turkey suggests that Galatasaray could take him off Liverpool's hands
Liverpool signed Gravenberch for $43m (£34m/€40m) in August and the club would not want to make a loss on him.
Liverpool.com says: It remains to be seen if Liverpool will want to offload Gravenberch after just a year at the club
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