The former Liverpool midfielder scored from the penalty spot during their 3-0 victory over Faroese side NSI Runavik in the first leg of their qualification stage of the European competition.
If Fulham were to repeat their success of the 2009-10 season when they found themselves in the final of the Europa League, then a further 22-games would have to be played on top of their domestic fixtures.
However, Murphy believes that if the players can maintain the Premier League as their primary target, then there will be no problems in keeping themselves in the top-flight.
"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 told reporters.
"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 win on Thursday was the first game with new manager Martin Jol in charge and the Dutchman has yet to add to the side he inherited from Mark Hughes.
Murphy is aware that the team could develop positively with the inclusion of new faces and is wary of losing focus in what matters to the club.
"The squad is as healthy as it has been in a long time in terms of quality," he added. "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]."