The Cottagers have endured a torrid run since earning promotion back to the Premier League at the first attempt courtesy of an extra-time victory over west London rivals Brentford in the Championship play-off final at Wembley in August.
An opening day thrashing by Arsenal was followed by further defeats to Leeds, Aston Villa and Wolves, while Parker’s side were also humbled by Brentford in the fourth round of the Carabao Cup.
While a 1-1 draw against fellow strugglers Sheffield United last weekend offered brief respite and at least saw Fulham get a point on the board, the losing swiftly resumed on Saturday as goals from Jairo Riedewald and Wilfried Zaha saw Crystal Palace emerge 2-1 winners at Craven Cottage.
Such a woeful start has provoked inevitable comparisons with Fulham’s miserable 2018/19 campaign, when they were relegated despite spending in excess of £100million in the transfer market.
Questions over Parker’s future are sure to grow louder if swift improvements are not forthcoming, with one point from six matches and 14 goals conceded ranking among the worst-ever starts to a top-flight campaign.
“I can’t control that,” Parker told Sky Sports when asked if he feared for his job.
“What I can do is what I have normally done throughout my career and life, during these hard times, it is the time to front up and keep working as hard as I can to get the rewards that I deserve.
“It is out of my hands but I will keep working hard.”