Damien Duff, Murphy and Andrew Johnson netted the all-important goals as recently-appointed manager Martin Jol enjoyed a 3-0 victory over Faroese minnows NSI Runavik in his first match at the helm.
Fulham have seemingly already dispatched NSI with a clinical display in the first leg of their first qualifying round clash, but a further 22 matches remain if they are to repeat the heroics of 2010 and make the final.
Thursday night's game also marked the start of an 11-month season for Jol and his men, which some fear could see them struggle for form and fitness in the Premier League.
Murphy admits competing in Europe has the potential to have a detrimental effect on their domestic campaign, although he insists the Cottagers will always put league success first.
"I think last time we did it - if I remember correctly - we put ourselves in quite a safe position (in the league) quite early on," he said.
"We were never ever in any trouble and I think the problems come if you are trying to fight a relegation battle.
"Or like last season where there were 10 teams up until probably the last month of the season fighting week-in, week-out.
"If you're trying to play European games as well then it could be problematic but let's hope we're not in that position.
"The squad is as healthy as it has been in a long time in terms of quality. We are lacking a few numbers - that's true - but they know that upstairs and they will be addressing it.
"But we've got to be careful not to get too focused on the Europa even though that is the focus at the moment, if you know what I mean?
"The Premier League is your bread and butter and the last thing you want to be doing is losing silly games and points because you're trying to progress in this competition.
"It is a fine balance but the manager gets paid big bucks for (making decisions like this)."
After seeing off NSI with relative ease at Craven Cottage, senior players like Murphy could be rested for next week's jaunt to the Faroe Islands.
And while the 34-year-old midfielder admits that progression is not yet a done deal, he expects Jol to blood a few youngsters in the second leg.
"It is a difficult one at 3-0," he said.
"If it was five than it would probably be a little bit easier.
"I would expect one or two of the younger lads to play maybe. Of course you need a spine [of senior figures] but the difference when you play away is that it can be a bit of a dodgy pitch, a bit of a different atmosphere and so on.
"It can only take one mistake and you're a goal down after 10 minutes and all of a sudden some of the younger lads might be like 'what is going on?' so you have to be a bit careful.
"Whatever team he plays, let's be honest, we should be comfortable with a 3-0 lead. They're not particularly good and as the game went on we should have wrapped it up more really.
"It will be used as a fitness exercise I imagine and I don't know whether he will take everyone or not. He will obviously be having a think about that over the next few days."