Savage said he doesn't want to hear anyone calling for the Liverpool manager's head after a difficult start to this season, with the Reds seemingly in transition this term.
He wrote in his Daily Mirror column: "If you take Luis Suarez and Daniel Sturridge out of Liverpool's team, of course, they are going to find it hard to adjust.
"Rodgers performed absolute miracles last season by finishing second and coming within a whisker of winning the title.
"Suarez jumping ship to Barcelona and Sturridge's injury are not Rodgers' fault. There may be the odd slip while Liverpool adjust to life without Suarez, but Rodgers will get it right. I still expect them to challenge for a top-four finish."
The Reds are just three points off the Champions League places at this early stage of the season, and it can easily be made up between now and the end of the campaign - and despite the defeat to Basel, the still have a good chance of qualifying from their group - though defeat against Real Madrid at Anfield at the end of the month could leave them in a tricky position.
They still have the League Cup open to them as they compete on four fronts this term, and Rodgers has spoken of his desire to deliver a trophy for the club in his third season at the helm.
With the loss of Suarez and nine players arriving at the club this summer, there was always going to be an element of 'bedding in' time. A win this weekend against West Bromwich Albion would leave the side in a stronger position going into the international break - and it does feel like a massive game for the side. But with sides with similar ambitions as Liverpool playing each other this weekend, it's a good opportunity to make up ground.