The former Fulham manager was confirmed as new boss at Anfield on Thursday morning.
Murphy said: “I admire Roy Hodgson. He has a philosophy of playing good football which will fit well at Liverpool.
“He gives players responsibility and a platform to work from.
“Maybe it is time Liverpool had an English manager who knows about the club.”
Murphy added: “Roy is a talented manager who succeeds because he works incredibly hard.
“He instils confidence in his players and has a style the players can enjoy.
“His success has been a mix of a lot of things but primarily hard work.
“He has real tactical knowledge too – in a way it has come from Roy’s Italian managerial roots, it is an Italian style.”