Felix Magath was sacked by Fulham owner Shahid Khan on Thursday, after the German guided the team to just one point from their opening seven matches following relegation from the Premier League in May.
Symons was appointed as a temporary replacement, but a change of leadership could not bring about an upturn in fortunes as they went down to Jordan Rhodes' solitary strike at Craven Cottage.
Fulham's Shaun Hutchinson was shown a straight red card in first-half stoppage time for a studs-up challenge on Lee Williamson, who had to be carried from the field on a stretcher.
Rhodes then stabbed home a loose ball in the 58th minute to complete Fuham's misery and ensure they stay rooted to the foot of the table.
Another side who axed their manager in the week fared slightly better, as Cardiff City drew 2-2 at Derby County after Ole Gunnar Solskjaer departed on Thursday.
Under the caretaker duo of Danny Gabbidon and Scott Young, the Welsh outfit looked set for all three points when Aron Gunnarsson and Peter Whittingham put them two goals to the good shortly after half-time.
But the hosts had other ideas, Jordan Ibe halving the deficit in the 61st minute, before Craig Bryson earned a point for his side six minutes from time.
Just above Fulham at the bottom are Blackpool, who earned only their second point of the campaign with a goalless draw at Brighton and Hove Albion.
At the opposite end of the table, Wolves gained ground on the leading pair of Nottingham Forest and Norwich City as Nouha Dicko's first-half goal sealed a 1-0 win over Bolton Wanderers, who were left to rue Owen Garvan's missed penalty in the second period.
The win for Kenny Jackett's side saw them move level with Norwich and a point adrift of leaders Forest after both sides were held.
Stuart Pearce's Forest drew 0-0 at Millwall, while Norwich fought back well from two down to force a 2-2 draw at home to Birmingham City, thanks to a brace from Cameron Jerome.
The most convincing winners of the day were Middlesbrough, who thrashed Brentford 4-0 at home, while Leeds United were similarly comfortable in seeing off Yorkshire neighbours Huddersfield Town 3-0 at Elland Road.
Both victors saw men sent off in Dean Whitehead and Gaetano Berardi respectively, but the dismissals came too late to have any bearing on the results.
Elsewhere, Sheffield Wednesday's strong start to the season continued with a 1-0 win over Reading, while the games between Rotherham United and Charlton Athletic and Watford versus Bournemouth ended 1-1.
