Hodgson had lambasted Benitez for his apparent treatment of the Liverpool legend, to which Benitez replied that Hodgson knew nothing of the situation and that the current Liverpool manager should concentrate on the job at hand.
Speaking to Sky Sports News, Hodgson agreed with Benitez that managers need to concentrate on the work at their own club, whilst also apologizing for any unintended offense he may have caused.
"I totally agree with him [Benitez] that every manager needs to work with his own club," the Liverpool manager said.
"If I have upset him by saying something which I certainly didn't mean to be in any way critical or negative about his work at the club, then I would happily apologize because there was never any intention to do that.
"As far as I am concerned I work at Liverpool and do my best for Liverpool, and he will work at Inter and do his best for Inter.
The former Fulham manager also refused to comment on opinions aired by certain members of the media, stating that he would accept any opinions without comment:
"I have no comments to make about other people's opinions - I'll allow them to make them and in this case I'll accept them if that's what they want to be," he concluded.