Liverpool are enduring a deeply disappointing season but the Anfield club knew that a win at home to Basel would take them through from Group B into the knock-out stage for the first time since 2009.
However, Basel, convincing winners when the sides met in Switzerland two months ago, needed only a point and a pinpoint strike by Fabian Frei in the 25th minute set them on their way.
"The expectation was to get through the group. We haven't done that because we haven't been good enough, but we'll learn from that," Liverpool manager Brendan Rodgers, whose side must now settle for the consolation of a place in the Europa League, told Sky Sports.
In contrast, Basel coach Paulo Sousa said: "We are working in this direction to achieve important things like we achieved today, which gives us the opportunity to challenge other fantastic teams."
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The draw for Juve means Olympiakos drop into the Europa League despite a 4-2 win in Greece against a Malmo side who finished with 10 men, with David Fuster, Alejandro Dominguez, Kostas Mitroglou and Ibrahim Afellay all scoring.
Meanwhile, it was a memorable night for Monaco, who needed only a point at home to Zenit St Petersburg to advance but a 2-0 win in the Principality, coupled with a 0-0 draw between Benfica and Bayer Leverkusen in Lisbon, saw them go through as Group C winners.
"Qualifying was important for me, but more so for the team, the Principality and for French football," said Jardim.