Down 3-0 from the first leg, Liverpool coach Jurgen Klopp deployed his best men from the opening whistle. Trent Alexander-Arnold, Luis Diaz and Mohamed Salah were in the starting line-up and Brazilian goalkeeper Alisson Becker was between the pipes.
Playing at home, coach Gian Piero Gasperini and Atalanta were still flying high after their huge victory at Anfield thanks to a brace from Italian striker Gianluca Scamacca and a goal from Croatian Mario Pasalic.
Liverpool came out aggressive and in the 5th minute, a penalty was whistled in favor of the visitors.
Egypt international Mohamed Salah appeared on the spot and beat Juan Muso, giving the Reds an early lead and narrowing the aggregate deficit to 3-1.
Shortly afterwards, Liverpool had an opportunity for a second goal. A through ball to midfielder Dominik Szoboszlai who was just a bit long and Musso got to the ball first.
Liverpool continued to press. A shot from Luis Diaz forced Musso to make a great clearance.
After the initial pressure from the English team, the home team came forward in attack with a valuable exchange between Scamacca and Aleksei Miranchuk that did not produce a positive conclusion.
A few minutes later, the Russian took a shot from outside the area but it did not worry Alisson.
By this time, the Liverpool players did not show the same freshness as in the opening minutes and limited themselves to managing possession in search of an opening. But Atalanta's careful defense allowed little space.
Before the half ended, Atalanta saw a Teun Koopmeiners goal disallowed for offside.
The second half resumed with Atalanta trying to slow the pace of the match via careful ball management.
Nonetheless, the home team took risks on two occasions.
First, a misreading of the ball's trajectory by goalkeeper Musso was cleared by the timely intervention of Sead Kolasinac. Later, the Argentine goalkeeper became a great protagonist with an extraordinarily important save from a Salah close-range shot.
The impressive Dutch defender Virgil Van Dijk powered a header from a free kick from Alexander-Arnold, but the attempt was calmly blocked by Musso.
Scamacca responded, as did Davide Zappacosta and, along with the slick off-the-ball movements of Dutch midfielder Koopmeiners, Atalanta got off a few shots, repeatedly challenging Alisson.
After the first hour of play, Klopp took off Diaz and Salah for Diogo Jota and Darwin Nuñez.
Gasperini reacted by sending on Charles De Ketelaere and Mario Pasalic.
Despite the changes, Liverpool appeared to have lost the conviction of being able to recover the result.
In fact, the defensive solidity of the Italian team combined with persistent pressing dampened the characteristic aggressiveness of the Reds who were no longer able to get close to the penalty area except through long passes which were easily cleared.
The match ended 0-1 but it was Atalanta who celebrated the deserved passage to the next round, an historic milestone. For just the second time, Atalanta will play in another European semifinal, the first coming 36 years ago in the 1988 Cup Winners' Cup.
Atalanta will face Olympique de Marseille who defeated Benfica in a penalty shootout in the semifinal.