Liverpool were unable to book a place in the last 32 of the Europa League with a game to spare after they were held to a 2-2 draw by Young Boys at Anfield on Thursday.
A late goal by Elsad Zverotic means the Reds' hopes of moving into the knockout stage of the tournament will now be decided in Italy against Udinese in two weeks' time.
Liverpool had taken a 33rd minute lead when Jonjo Shelvey headed home from close range following crisp play between Suso and Joe Cole.
Young Boys levelled through Raul Bobadilla shortly after half-time when the striker arrowed into the back of the net from a tight angle.
Cole regained Liverpool's advantage when he finished neatly at the Kop end on 72 minutes after being teed up by substitute Steven Gerrard, but with time running out Zverotic drove home an equaliser for the Swiss side.
The pre-match team news confirmed several changes for Brendan Rodgers' men, including a three-pronged attack consisting of Oussama Assaidi, Cole and Shelvey.
Meanwhile, it was a landmark night for Pepe Reina who started between the sticks to make his 81st European appearance for Liverpool, breaking Ray Clemence's long-standing club record.
Following Anzhi's 2-0 success over Udinese earlier in the day, the Reds walked out onto the Anfield turf aware a win would seal a place in the last 32 of the competition with a game to spare.
However, harbouring their own hopes of progress, it was the visitors who instantly went on the attack, with Gonzalo Zarate improvising to hook over the bar with just nine seconds played.
Next, Raphael Nuzzolo received the ball at the end of a Young Boys counter-attack and stung the palms of Reina with a left-footer from just inside the area.
Having weathered the Swiss side's early exuberance, Liverpool began to set about dictating play and commanding possession - though goalkeeper Marco Wolfli wasn't troubled until the 17th minute when Shelvey's clever pass sent Cole scampering into the right-hand channel of the box before striking wide of the far post.
The stopper was required to collect a Jordan Henderson free-kick low to his right soon after, while down the other end, Martin Skrtel needed to be at full stretch to block Alexander Farnerud's effort from inside the home side's area.
Wolfli's involvement in the contest was increasing and on 26 minutes only his fine stop denied Liverpool a picture book opener after Shelvey's sumptuous flick allowed Jordan Henderson to motor into the box and drill goalwards.
With half an hour played, Gerrard entered the action to replace Andre Wisdom with the young defender having picked up a knock. Henderson reverted to right-back as part of the re-shuffle.
And within moments, Liverpool were ahead. Cole and Suso swapped passes on the edge of the box to engineer an opening, and the former lifted the ball over the advancing goalkeeper to allow Shelvey to head over the line from inches out.
It was nearly two soon after when Martin Skrtel diverted Cole's effort goalwards from a corner, but Raphael Nuzzolo was on hand to hack off the line.
Liverpool were now in complete control and went close again to securing a two-goal half-time advantage when Suso steered wide with just Wolfli to beat and the interval looming.
Young Boys emerged with renewed optimism following the break and after Farnerud had drilled over Reina's bar Zverotic swerved inches off target from distance.
Back came the Reds and Suso's precise through ball dissected the visiting defence, but Cole could not beat Wolfli when one-on-one - and it would prove a costly miss as the Swiss club drew level within seconds.
Farnerud's raking pass picked out Bobadilla just inside the box. The No.9 took a touch to set himself before blasting across Reina into the far corner with a fine finish.
The game now delicately poised, Luis Suarez made his entrance with an hour played to take the place of Suso.
By now, Liverpool were firmly back in the ascendancy and they pinned their guests back with a succession of corners in front of the Kop.
A breakthrough seemed inevitable - and it duly arrived with 18 minutes left to play.
Suarez and Gerrard's slick exchange of passes allowed the latter to pick out Cole's run into the box. With his back to goal, the No.10 spun before stabbing beyond Wolfli and wheeling away in celebration.
But with time running out, Zverotic claimed an equaliser for the visitors by blasting home from the edge of the box, meaning Liverpool's Europa League fate now rests on the outcome of the trip to Udinese in a fortnight's time.
Liverpoolfc.com journalists' man of the match: Jonjo Shelvey