The USA international became the all-time leading Premier League scorer for the Cottagers this season with his tally of 12 taking his overall count to 33, bypassing Frenchman Steed Malbranque and fellow American Brian McBride.
But Murphy said it was more than just goals which makes Dempsey stand out from the rest.
“I think people forget just what Clint can bring to a side,” said Murphy speaking to fulhamfc.com. “We know that he has a lot of skill and is one of those players that can make things happen out of nothing.
“But there’s more to his game. He tracks back, he wins tackles and is a valuable outlet when under pressure. I think he’s the longest-serving player in the current squad and that’s testament to his ability and how much he means to the Club.
“For me, last season he was terrific – he really stood out.”
And Murphy went on, saying that the attacking midfielder did a tremendous job in the absence of more noted attackers Bobby Zamora, Moussa Dembélé and Andy Johnson.
“Clint was probably the mainstay of our strike force for long periods of the season,” explained Murphy. “We had a lot of injuries to our forwards with Bobby joined by Mousa Dembélé and Andrew Johnson for long periods.
“As a result a lot of pressure was put on his [Clint’s] shoulders and he did extremely well. If it wasn’t for his goals and desire to do well, at what proved to be a difficult time, then things could have been very different for us.
“He’s a player that has a habit of being in the right place at the right time, and that was very evident last season. It was difficult having so many of the forwards missing, because let’s be honest, they are the team’s main source of goals.
“But Clint stepped up and relieved the pressure. I think he can be very happy with how he played last year and to become the Club’s leading Premier League goal scorer shows the contribution that he has made since he came in.”