New manager Martin Jol enjoyed a winning start with last week's 3-0 victory in their first qualifying round first leg clash at Craven Cottage, where Murphy netted from the spot.
However, Murphy maintains the squad cannot think the job is already done as their build-up to the new domestic campaign continues in unlikely surroundings of Torshavn in the Faroe Islands.
"It is a difficult one at three-nil. If it was five it would probably be easier. I would expect one or two of the young lads to play maybe," Murphy told the club's official website. "Of course you need the spine of the team, but when you play away it could be a dodgy pitch and it only takes one mistake and you can be a goal down after 10 minutes.
"You have to be careful, but let's be honest, whatever team we play we should be comfortable with a three-nil lead.
"As the game went on at the Cottage we should have scored more goals and wrapped it up."
Fulham were handed the opportunity to compete in Europe via UEFA's Fair Play League, but still have a long road ahead before they can contemplate tackling the group stages.
Having reached the 2010 Europa League final under Roy Hodgson, Murphy would welcome another shot and believes progression through the qualifiers should see Jol's men hit the ground running for their opening Premier League game against Aston Villa.
"It is a positive that we have got the opportunity to play in Europe again," said the former Liverpool, Charlton and Tottenham midfielder.
"Not everybody is used to doing it so it's going to be a test, but you've got to look at the positives, and the run of two years ago will live long in the memory of everybody associated with Fulham, so why not go on a good run again?
"In July you're playing friendly matches anyway, trying to get fit, so if anything we will be ahead of schedule.
"We might have some tired legs at the end of the season, but then it's down to the manager to rotate players.
"Last time we did it we put ourselves in a safe position fairly early on and we were never in any trouble.
"The problems come if you're trying to fight a relegation battle whilst playing European games.
"Let's hope we're not in that position.
"The squad is as healthy as it's ever been in terms of quality. We are lacking a few numbers and I am sure that will be addressed."
Fulham have been linked with an £8million move for Barcelona forward Jeffren, also on Liverpool's radar.