The Cottagers finished 12th last term but have endured a torrid time at the start of 2013/14, winning just three and losing six of their opening 10 league games.
The West London club are currently two points clear of the drop zone courtesy of back-to-back victories over Stoke and Crystal Palace, but fans remain restless after a first half horror show at home to Manchester United last weekend.
Fulham face another tough test on Saturday against one of Murphy’s old clubs, Liverpool. But the 36-year-old, who made more than 200 appearances for Fulham and reached the Europa League final, believes they have the personnel to extend their Premier League stay into a 14th campaign after promotion back in 2001.
Speaking exclusively to FourFourTwo, Murphy said: “I don't think they need to worry about being relegated. When you look at teams down the bottom you associate them with a lack of goals. I think with the likes of Darren Bent and Dimitar Berbatov at the club they've got enough of a goal threat.
“If they can tighten up and make themselves harder to beat I think results will improve. The depth of the squad isn't as strong as it was a couple of years ago and hopefully the new owner can help Martin address that.
“It's not a time for clubs to panic and sack managers after 10 games in my opinion. Martin will sort it out.”
ALSO ONLINE Murphy: Suarez-Sturridge combo best in Europe
INTERVIEW Murphy: Rodgers must improve Liverpool's midfield
‘After Manchester City’s recent form, maybe they’re the underdogs against Manchester United!’ Former Red Devils defender on this weekend’s derby
‘Arteta, Alonso, Emery, me… none of us were physical players – we needed the understanding of the game. That probably helped us move into management’: Premier League boss reveals reasons for natural career progression
