Liverpool forward Sterling dropped to the bench for England's Euro 2016 qualifier against Estonia last Sunday, with manager Roy Hodgson stating the teenager had told him he was suffering from fatigue.
Sterling, who came off the bench in Tallinn and was upended for the free-kick which Wayne Rooney scored to secure a 1-0 win, has come in for criticism this week, but Liverpool boss Rodgers revealed it was Hodgson's decision to leave him out.
Hodgson called into question Liverpool's policy of players not taking part in full training sessions until three days after a game and is reported to be eager to speak to Rodgers at Sunday's Premier League clash against QPR.
Rodgers has leapt to the defence of Sterling and dismissed talk of a rift with the England boss.
He told The Independent: "I'm fed up reading about this club v country row, claims we intervened and put pressure on Roy Hodgson.
"I've read we sent dossiers to the FA [Football Association] on Raheem Sterling and Daniel Sturridge and I'm having showdown talks with Roy Hodgson on Sunday and all sorts of rubbish.
"The decision not to play him was a managerial decision. I haven't said a single word but have to say I have never seen such rubbish written over the last few days.
"At no point did Raheem Sterling say he didn't want to play for England. The boy is being hung out to dry and I dare say the criticism will continue for a few more weeks to come because of this."
The former Swansea City boss added: "Let me tell you, there have been at least five occasions in the past when Raheem has said he felt tired before games but he's never refused to play.
"We have taken on board what he has said and taken a decision accordingly. I rested him against Aston Villa and we lost the game. But it was our decision to do so – and our decision alone.
"Last season he said he felt tired before the Manchester City game. We won 3-2 and he put in a man-of-the-match performance.
"The point I'm making is you have to take on board advice from your own people and make your own decision, right or wrong."
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