Gerrard curled the ball into the top corner with eight minutes remaining to cancel out Fabian Frei's rasping first-half drive, but the Premier League side, who had been reduced to 10 men following the second half sending off of Lazar Markovic, could not find the crucial winner.
Barring their late flurry, it was a largely a dismal home performance from Liverpool who finished third in Group B on five points, two adrift of second place Basel.
Liverpool, whose poor start to the season shows no sign of improving, will now drop into the less demanding Europa League.
Liverpool boss Brendan Rodgers may have hoped the occasion would spark an improved attacking performance from his struggling side, but within minutes of the kickoff it was very much business as usual as the visitors grabbed the upper hand over their nervy hosts.
It took only 12 minutes for Basel to craft an early sight of goal as Shkelzen Gashi found a pocket of space on the edge of the area but slashed his shot wide.
That proved to be an unheeded warning as Liverpool retreated further into their shell and Basel grew in confidence before taking the lead in stylish fashion on 25 minutes.
After some crisp and careful passing around the edge of the Liverpool area, the ball was touched back to Frei, who flashed a daisy-cutter across the Anfield turf and into the back of Simon Mignolet's net with the Liverpool keeper rooted to the spot.
The match threatened to turn into a horror show for the hosts as Basel spurned further chances with Marco Streller spooning a volley off target and Gashi rippling the net once more with an offside flag sparing Liverpool's blushes.
Rodgers hauled Alberto Moreno and Markovic off the bench in an effort to inject some urgency, but the latter's night lasted just 15 minutes as he was sent off for flicking out his hand and catching the face of Behrang Safari who dramatically tumbled to the ground.
Referee Bjorn Kuipers angered the Liverpool fans further by denying Gerrard a penalty when he tumbled under the challenge of Basel keeper Tomas Vaclik, minutes before the Liverpool midfielder picked his spot superbly with a free kick from the left-hand edge of the area.
(corrects headline to strike from strikes)
(Reporting by Toby Davis; editing by Brian Homewood)
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