The Cottagers have defied all odds during their arduous 10-month march to the Hamburg Arena by producing a string of giant-killing displays.
Big-spending holders Shakhtar Donetsk, Italian giants Juventus and German champions Wolfsburg are among the victims strewn across the 18 matches it has taken to reach the final.
Dan the man: Murphy is desperate to finish the job against Atletico Madrid
Universally acclaimed for reaching a European showpiece and doing it the hard way, Fulham are braced for the biggest match in their 131-year history.
But Murphy insists the plaudits will sound hollow unless they claim the club's first major piece of silverware.
'Even though we deserve the praise we're getting, it won't make it feel any better if we wake up on Thursday morning without having won the trophy,' said the club captain.
'It's great to be in the final but we want to win and complete the fairytale. If we manage that we can be pleased with ourselves and look back with huge satisfaction on a wonderful season.
'For us to win would be an unbelievable achievement. To do what we've done is remarkable with the squad and the budget we have.
'We know it will be difficult because that's the way it's been in every match of this competition.'
Mirroring virtually their entire European campaign, Fulham are expected to be up against it one last time after bookmakers installed Atletico as clear favourites.
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Roy Hodgson's side have spent the season making a mockery of predictions so another upset would hardly be surprising, but Murphy insists Atletico start in pole position.
The Spanish club may sit in mid-table of La Liga but they have also reached the final of the domestic cup and bristle with attacking options in Sergio Aguero, Jose Antonio Reyes and Diego Forlan.
'I wouldn't understand if people made us favourites. You have to base it on the players the team has and the budgets they work from,' he said.
'I'd hazard a guess that Atletico's wage bill is far greater than ours. They have a lot of top-class international players
'We deserve respect for what we've achieved but they're still the favourites. That's no problem to us anyway, we're used to it now. If we play well we can beat anybody.'
Murphy helped Liverpool win the 2001 UEFA Cup but insists Fulham's European adventure is a greater achievement.
'There's a big difference - at Liverpool you're expected to be in finals every year,' said the 33-year-old midfielder.
'When we started out on this campaign even the die hard fans probably didn't anticipate such a wonderful run to get to the final.
'This is a different type of satisfaction. The expectancy hasn't been there and the underdog tag has stuck with us throughout the competition.
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'A good analogy is that the other day Liverpool were talking about winning the Europa League as a consolation.
'We're talking about it being the best trophy in the club's history.'
Fulham are waiting for injury updates on striker Bobby Zamora and winger Damien Duff, who face a race against time to be fit from their respective achilles and leg problems.
'Hopefully Bobby and Damien will be fit,' said Murphy. 'It would be a shame if either of them were to miss out because they've contributed so much to this season.
'They've been two of our best players so it's fingers crossed because you want your best team available.'
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