The Swiss side had beaten Manchester United, Chelsea and Tottenham in the last four years and added the Merseysiders to their list of scalps as Marco Streller scored the only goal of the game in the 53rd minute.
Rodgers felt his side played well enough to get something from the game but let themselves down by failing to deal with Basle’s set pieces.
“We defended very, very poorly on the corner and it’s not the first time so it’s very, very disappointing we couldn’t get something from the game and the game was decided by a poor defensive corner,” he said.
Mario Balotelli often cut an isolated figure up front in the sole striker role but despite failing to find the net for the fourth game running, Rodgers thought the £16 million (€20m)summer signing played well.
“He worked hard, (but) needs to do more,” Rodgers said of the Italy striker. “He will be judged on what he creates and what he scores and he didn’t score.
“The boy is trying, he is working hard.”
Basle, watched by Germany manager Joachim Low who lives nearby, attacked with pace and controlled possession and no shortage of aggression.
In fact the only black mark for the hosts came in the first half when referee Jonas Eriksson halted play to retrieve a missile thrown from their hard-core fans behind one of the goals.
Liverpool never really threatened Tomas Vaclik in the Basle goal and that was not just down to the absence of Sturridge, who has missed the last six matches with a thigh injury but could return against West Brom at the weekend.
Balotelli began by appearing like he was starting to look more comfortable in the spearhead role, holding up the ball well and linking play, particularly with the overlapping Javi Manquillo — a combination which managed to pick out Raheem Sterling, only for the forward to be flagged offside before his shot against the post and converted rebound had registered.
However, Balotelli became increasingly isolated up front and still does not offer enough in the way of work-rate and movement for Rodgers and on more than one occasion the manager registered his displeasure that the Italian was not working harder for his team-mates.
The better of the chances fell to Basle, who looked to expose the space behind Liverpool’s advancing full-backs — particularly the left-sided Jose Enrique who allowed Derlis Gonzalez, an early substitute for the injured Behrang Safari, to get the wrong side of him only for his poor first touch to knock off the end of the pitch.
Mignolet, who has come in for increasing criticism recently, dealt comfortable with Basle’s first shot from Mohamed Elneny and then blocked Geoffro Serey Dey’s effort after he side-stepped Enrique and Dejan Lovren far too easily but he was relieved to see Ahmed Hamoudi’s fierce angled attempt flash past his far post. Lovren was only slightly more effective at the other end, missing two good chances with his head from Philippe Coutinho set-pieces.
Sterling also failed to trouble goalkeeper Vaclik sufficiently after Jordan Henderson’s raking crossfield ball dropped to him just before half-time.
The England winger’s block on Gonzalez five minutes into the second half had home fans screaming for a penalty but Eriksson did not agree.
Mignolet came to his side’s rescue moments later saving low from Hamoudi but Lovren’s panicked concession of a corner proved costly as Liverpool were exposed yet again at a set-piece as the goalkeeper clawed out the flick on from Taulant Xhaka’s corner but could not prevent Streller smashing home from close range.
Liverpool’s response was a viciously dipping 35-yard Balotelli free-kick which Vaclik parried into the path of Lazar Markovic whose follow-up was blocked, although the 20-year-old Serbian was far more culpable in missing the target from Enrique’s low cross with 14 minutes to go.
Even Steven Gerrard, who scored an added time winner to get their campaign off to a winning start at Anfield against Ludogorets, could not rescue a point with a late free-kick straight at Vaclik.
The final whistle brought huge cheers – and jeers as Balotelli turned on his heels and marched straight down the tunnel without a second glance behind him. The 24-year-old still has plenty to learn if he is to come anywhere close to become the striker Liverpool expect him to be.