Murphy, Hodgson's captain at Fulham last season, is backing his old boss to turn things around at Liverpool and to quickly get the Reds climbing the Premiership table.
"The way he wants his team to play and the type of tactics and discipline he wants his team to have don't happen overnight," said the former Red.
"Of course the Blackpool and Northampton results were unacceptable. I'm not hiding behind that. All I'm saying is the situation is not dire. The league table is separated by five points from third-bottom to fourth, so there's a long way to go.
"Stay patient, the team has quality in it. Give Roy a bit of time and by Christmas see where we are and everyone will be happier."