Jurgen Klopp's side were eliminated from Europe's secondary competition despite prevailing 1-0 in Bergamo, having fallen to a chastening 3-0 loss at Anfield in last week's first leg.
The Merseyside giants exploded out of the blocks and were rewarded for their quick start with just seven minutes on the clock, as Mohamed Salah crashed home a penalty after Matteo Ruggeri's handball from Trent Alexander-Arnold's cross.
The Egyptian squandered a brilliant chance to cut the aggregate deficit further later in the first half, though, as his lob over Atalanta goalkeeper Juan Musso — caught in no man's land — bounced the wrong side of the post.
However, Liverpool were a shadow of their first-half selves in the second 45, where they fired just two shots on the Dea goal for an Expected Goals (xG) of 0.11 to ultimately exit with a whimper.
Van Dijk praises «great fight» in Liverpool exitDespite the lackadaisical nature of the visitors' second-half performance, Van Dijk — speaking to TNT Sports — believed that the Reds showed «great fight» to prevail on the night, even if their triumph was inconsequential.
«Firstly credit to Atalanta. Last week we were very poor and they had a good game. They deserved to go through because we made it far too difficult for ourselves,» the Liverpool captain said.
«Tonight was a good game and we showed great fight. It was an improvement but the reality is we are out and we have to very quickly recover and travel to London on Saturday.
»We tried and we had opportunities. At times we wanted it too quickly as everyone was
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