Gerrard was left out of the first 11 for the match at Anfield as Liverpool arrested a run of three consecutive Premier League defeats with a nervy and hard-fought 1-0 victory that arrived courtesy of a late goal from Glen Johnson.
It was the 16th anniversary of the 34-year-old midfielder's debut for the Merseyside club and he was keen to play down a reported rift.
"Just to set the record straight media talk of a fall out between us 2 is NONSENSE ..have a nice Sunday," he wrote on Instagram, accompanying a picture of him and Rodgers in training.
Gerrard came on as a late substitute in a more attacking role as Liverpool went in search of the opening goal, having largely dominated the match without finding a breakthrough.
Liverpool manager Rodgers had preferred Lucas Leiva in the anchor midfield position that Gerrard has recently occupied as he sought to help plug holes in a leaky defence, as well as handing a well-earned rest to his captain who had been a virtual ever-present.
Gerrard's role had come under scrutiny from fans and pundits this season as teams sought to nullify his influence and curb his ability to pull strings from a deep midfield position.
Without the incisive running of strikers Luis Suarez, who joined Barcelona in the close season, and the injured Daniel Sturridge, Gerrard's trademark long passes have often lacked a target, reducing his influence in the quarter-back role.
The introduction of Lucas, as well as Kolo Toure at centre back, seemed to shore up Liverpool's rearguard, and both drew praise from Rodgers in the wake of Saturday's clash.
"Lucas Leiva has come into the team and been outstanding in his two games -- very tenacious, aggressive and can pass the ball. Kolo Toure's experience coming into the team has been good for us," the manager told reporters.
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