Gerrard's exquisite late free-kick cancelled out Fabian Frei's 25th-minute opener, but with Liverpool reduced to ten men by the dismissal of substitute Lazar Markovic, Paulo Sousa's Basel held on for a point that took them into the last 16 alongside Group B winners Real Madrid.
It was yet another English scalp for Basel, who knocked Liverpool out of the tournament in 2002, eliminated Manchester United in 2011, put Tottenham Hotspur out of the Europa League two seasons ago, and beat Chelsea twice in the Champions League last year.
"For me and my staff and the players, it's special," said Sousa.
"We are working in this direction to achieve important things like we achieved today, which gives us the opportunity to challenge other fantastic teams."
The match fell ten years and a day after Gerrard had inspired Liverpool to a stirring 3-1 win over Olympiakos at the same stage of the competition, en route to an unforgettable comeback against AC Milan in the final.
But his fine 81st-minute strike was not enough to rescue his team on this occasion as Liverpool's return to Europe's elite competition after a five-year absence dissolved in the Anfield drizzle.
"I don't think we deserved better," Gerrard told ITV Sport.
"We have not gone out because of this performance. We weren't good enough away to Basel (losing 1-0) and we let in a silly goal away to Ludogorets.
"You qualify over six games and we have not been good enough."
Brendan Rodgers must now rouse his side for a trip to old enemies Manchester United on Sunday, but the disappointment of a campaign in which his side's only win came against Bulgarian newcomers Ludogorets Razgrad will take some time to digest.
"We have to fight going forward to be in this competition next season," said Rodgers.
"We are not too far off the top four and, if we get there, we will be better in it next season."
Rodgers had emphasized the importance of patience prior to kick-off, but in front of an anxious crowd, the hosts were eager to get forwards quickly.
Captain Gerrard, back in the team at number 10 after being rested for Saturday's 0-0 draw with Sunderland, saw an early effort easily held by visiting goalkeeper Tomas Vaclik.
But there was haste and imprecision in Liverpool's attacking interplay and Basel began to exploit their nervousness, with Shkelzen Gashi slashing wide from Luca Zuffi's pass before Sousa's side went ahead.
Liverpool allowed the visitors to advance to the edge of their box and paid the price when Frei exchanged passes with Zuffi before crashing a 20-yard shot into the bottom-right corner.
Rodgers introduced Markovic and Alberto Moreno at half-time and the former's direct running provided Liverpool with a spark, only for him to be sent off on the hour for swinging a hand at the chasing Behrang Safari.
The Serbian winger did not appear to make contact with his opponent, but the intent was sufficient for Dutch referee Bjorn Kuipers to brandish a straight red card. Rodgers called it "an awful decision".
Taulant Xhaka had shot narrowly wide after striding to the edge of Liverpool's box immediately prior to Markovic's dismissal, but despite being a man down, the hosts belatedly began to offer a threat.
Martin Skrtel sent an audacious shot narrowly wide from 35 yards, while Vaclik showed impeccable timing to slide out and prevent Gerrard from surging onto Raheem Sterling's through-ball.
With nine minutes remaining, Gerrard set up a grandstand finish by arcing a picture-perfect free-kick into the top-left corner from just outside the box.
But in a frantic finale, an injury-time drive from Jordan Henderson that forced a full-length save from Vaclik was the closest the hosts came to the goal they craved.