Murphy has been linked with a return to Fulham in a coach capacity.
"I had an honest conversation with Murph and just explained to him that I want to move the football club forward, I want to think about the future of the football club," Appleton said.
"I explained that I was going to make Scott the new captain because I think he's someone who leads by example.
"It was a difficult decision to make but I think it's one that's going to benefit everyone at the football club. Danny took it very professionally, as I expected him to do."