The England midfielderâ€™s dream move from Chelsea has turned sour as Cole has experienced what he described as â€˜the worst run of form of my careerâ€™.
Cole has never operated in the position he thought had been earmarked for him â€” in the â€˜holeâ€™ behind Fernando Torres â€” but Hodgson believes that is a flimsy excuse for the 29-year-oldâ€™s failure to produce.
"He has got to do it on the field of play," said Hodgson. "Joe is a midfield player â€” what is the right position for a midfield player? Steven Gerrard has played all over the midfield for as long as I can remember. He is a good footballer and knows how to play.
"Steven would have been fit to play against Fulham. It doesnâ€™t hurt to have an extra week to get some training in but what he needs now is matches.
"Joe has got to come to terms with the fact he has come here after an unsuccessful period at Chelsea with high hopes of taking Liverpool by storm but, unfortunately, it has not worked out like that. But thatâ€™s life.
"He should have great confidence in his ability because he is a very good footballer. He should be looking to convince myself and everyone else that he is a player who can help Liverpool win. He couldnâ€™t say that has been the case so far.
"But he is training well and his confidence is returning. A good game and a goal or two could turn things around. But our group is getting stronger and the only thing I could say at the moment is, 'We are happy to have you, Joe, but I canâ€™t offer you anything more than a chance'.
"It is up to him to take that chance when it comes along. I have not lost faith in him. But I canâ€™t deny that the start he would have liked has not materialised."