Liverpool harboured frustrations Hodgson revealed Sterling had complained of tiredness ahead of the Estonia clash, that England eventually won 1-0.
Hodgson attended Sunday's Loftus Road thriller, but left 10 minutes before the end - and the entire calamitous climax.
Former Swansea boss Rodgers said he did not know whether England using Sterling sparingly in the last fortnight boosted his performance at QPR.
Rodgers said there was no need for him or Sterling to meet up with Hodgson on Sunday.
"I haven't thought on that a lot to be honest, there has been a whole series of things said and written about an unfortunate incident," said Rodgers.
"But we have to move on from that.
"I was actually quite busy believe it or not today, so I haven't had the chance (to speak to Hodgson).
"The kid's played the game and now he's having a shower - so I don't think he'll see him - not unless Roy's having a shower!
"We always talk, there's no fallout, there's no nothing.
"I'm not a barrier for England, if anything I'm a big supporter of the home nations and every country. I like to think I develop players that will hopefully develop national teams.
"So there's no issue, Roy and I speak and communicate well, we'll always find time to speak.
"He's a good man: I will always be here to support and help them."
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