Gerrard, who has made a habit of digging Liverpool out holes during a magnificent Anfield career, curled a sublime free kick 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 winner they required.
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. Real Madrid were runaway group winners.
Liverpool, whose poor start to the season shows no sign of improving, will now drop into the energy-sapping Europa League, leaving Gerrard to contemplate where his side had fallen short on their return to Europe's elite competition.
"I don't think we deserved better," he told ITV Sport.
"We have not gone out because of this performance... You qualify over six games and we have not been good enough."
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.
Basel flashed an early effort off target and Liverpool, so off the pace in the Premier League, retreated into their shell, before Basel took the lead in stylish fashion on 25 minutes.
After some crisp and careful passing around the edge of the 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.
Rodgers hauled Alberto Moreno and Markovic off the bench in an effort to inject some urgency, but the latter's night lasted only 15 minutes.
He was sent off for flicking out his hand and catching the face of Behrang Safari who dramatically tumbled to the ground, drawing the ire of the Liverpool manager.
"I thought it was an awful decision, I thought the referee was poor tonight to say the least," Rodgers said.
"The referee has seen the lad lying on the floor holding his face, but I don't know if he has seen the actual incident."
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 later the Liverpool midfielder picked his spot superbly with a free kick from the left-hand edge of the area, but there was little else to cheer for the home fans.
