Murphy has joined the Glasgow outfit on loan from the Seagulls and the deal is set to become a permanent switch in the summer.
The 28-year-old hopes to win silverware during his time at Ibrox and he is keen to help Rangers make a mark in Europe.
“I want to win trophies, that is what everyone wants to do in their career. I want to achieve things and to win things,” the forward told The Scotsman.
“You want to be remembered when you do eventually leave. That is what Rangers are all about – trying to win things.
“I have always enjoyed playing in Europe. I have been lucky enough to play in a good Motherwell side who got into Europe a couple of times. I got a few goals also which was good.
“European ties are massive for players and the club so that is an aim. That is all Rangers have ever known and is what we are trying to achieve. I am sure I am no different to anyone else in that dressing room.”
Pedro stepped off the bench to send Chelsea into the FA Cup semi-finals after they beat Leicester 2-1 at the King Power Stadium on Sunday evening.
RB Leipzig came from behind at the Red Bull Arena to end a run of four winless games and defeat Bundesliga leaders Bayern Munich 2-1 on Sunday.