Gianluca Scamacca netted a brace for the visitors, while Mario Pasalic was also on the scoresheet, as the Italian side placed themselves in an excellent position to reach the semi-finals of the competition, with the two teams set to lock horns for the return fixture next week.
Liverpool goalkeeper Caoimhin Kelleher kept out an effort from Pasalic in the third minute, with the Premier League club's number two using his face to make the stop.
Darwin Nunez was next to try his luck in an end-to-end start, but the Liverpool forward's fourth-minute effort was saved by Atalanta stopper Juan Musso.
Alexis Mac Allister then hit one over the crossbar in the fifth minute, before Nunez struck wide of the target in the 15th minute after being released into a promising position by Curtis Jones.
Harvey Elliott came incredibly close to making the breakthrough in the 26th minute, with the midfielder's curling effort from a wide angle coming off the crossbar in a huge left-off for Atalanta.
Liverpool were controlling the match, but Atalanta took the lead in the 38th minute through Scamacca, who silenced Anfield with a low finish under Kelleher after meeting a cross from Davide Zappacosta.
Teun Koopmeiners came close to doubling the away side's advantage in the closing stages of the first period, but the midfielder's effort was saved by Kelleher, with the referee's whistle blowing at 1-0 to Atalanta.
Liverpool dominated the possession in the opening 45 minutes, having 68% of the ball, but it was a story of missed opportunities and not for the first time in recent weeks.
Dominik Szoboszlai and Mohamed Salah were both introduced for the Reds at the interval, and the home side did make a lively start to the second period.
Virgil van Dijk glanced a header wide of the target in the 52nd minute, but Atalanta continued to look dangerous on the break, with Koopmeiners forcing Kelleher into another smart save in the 54th minute.
Musso made two excellent stops in quick succession to deny Salah less than a minute later, before Nunez lifted another attempt over the crossbar just before the hour.
Atalanta doubled their advantage just past the hour, with Scamacca netting his second of the match, placing a first-time finish past Kelleher after being found by Charles De Ketelaere.
Koopmeiners just missed the target in the 65th minute, with the Italian side going in search of a third, before Joe Gomez missed the target down the other end in the 71st minute.
Atalanta incredibly made it 3-0 in the 83rd minute, with Pasalic getting his name on the scoresheet, slotting into the back of the net from close range after Kelleher had denied Ederson.
Musso made another smart save to deny Luis Diaz in the 85th minute, before Diogo Jota and Salah took it in turns to miss the target in the 89th minute at Anfield, and Liverpool now have a mountain to climb if they are to progress to the semi-finals of the Europa League.