Spain midfielder Saul Niguez struck the only goal of the game in the fourth minute by bundling into the net from close range following a corner.
Champions League holders Liverpool will need to summon another famous European comeback at Anfield next month after they were beaten 1-0 away to Atletico Madrid in their last-16 first leg on Tuesday.
Spain midfielder Saul Niguez struck the only goal of the game in the fourth minute by bundling into the net from close range following a corner, their traditional weapon of choice in recent years.
Liverpool, who have won 25 of 26 Premier League games this season and are on course for a record-smashing title win, missed a series of chances to equalise in the second half, with Mohamed Salah and captain Jordan Henderson coming closest to scoring.
Juergen Klopp's side play at home to Atletico on March 11 in the return leg at Anfield, where they produced an incredible 4-0 win over Barcelona in last year's semi-final second leg after losing the first match 3-0.
"We gave them the best possible start and that gets the fans behind them and then they start falling over and getting under the skin a bit," Liverpool defender Andrew Robertson told reporters.
"We put in a decent performance and we know we can be better. We've got a second leg to put it right. They celebrated as if they won the tie after the game. They are coming to Anfield and we know our fans will be there."
Diego Simeone's men have looked nothing like the sides that reached the 2014 and 2016 Champions League finals and challenged Real Madrid and Barcelona's duopoly of La Liga for most of this campaign. They trail league leaders Real by 13 points.
But on Tuesday they produced a vintage defensive display, sitting deep and barely giving Liverpool any space for their attacking trident of Salah, Roberto Firmino and Sadio Mane to work their usual magic.
"This is the result of hard work and what happens when you never stop believing but keep on going," match-winner Saul told reporters.
"We have kept on working even though no-one believes in us and wants to bring us down. I celebrated the goal with so much passion because I was so up for the game, we have been criticised a lot but luckily I was able to help us out."
Atletico's Wanda Metropolitano stadium was the scene of Liverpool's 2-0 triumph over Tottenham Hotspur in last year's final but they faced a very different type of atmosphere this time around.
Clouds of billowing red smoke greeted the Atletico bus when it arrived at the ground as the home supporters stoked up a scorching atmosphere throughout the game to give their side a lift in the middle of their worst season in recent memory.
The home side were happy to let Liverpool dominate possession but despite having 73% of the ball, Klopp's side did not manage a single shot on target, although Atletico defender Felipe did block a goalbound shot from Salah in the first half.
Atletico only had one other attempt aside from their goal, when Alvaro Morata fired straight at the legs of Liverpool goalkeeper Alisson.
Liverpool forward Mane was fortunate not to be sent off late in the first half after clashing with Sime Vrsaljko while on a yellow card and he was swiftly substituted by Klopp for Divock Origi, who scored the second goal in last year's final.
He caused little disquiet to Atletico's towering defenders, yet Salah should have levelled with a header which went wide of the near post, while Henderson also narrowly missed the target from inside the area later on.