Chappell said: "There is nothing true in the rumours that his job is under threat. Alan is still under contract with the club.
"Fans are allowed to express their opinions — that's the point of football, so I can understand their views.
"But there has been no discussion or thoughts about changing managers. Alan Pardew is our manager and he will be for a long time to come yet."
Supported by TV income, Charlton had a huge wage bill when they were in the Premier League and relegation led to some serious cutbacks.
The sales of stars such as Darren Bent to Spurs, Andy Reid to Sunderland and Luke Young to Middlesbrough raised more than £22million and the parachute payments have also helped steady the ship.
Nevertheless, with the club's directors focused on long-term financial stability, Pardew has been forced to bring in new players from the lower leagues, such as Stuart Fleetwood from Forest Green Rovers and Nicky Bailey from Southend United.
Chappell added: "There are always financial constraints when a club gets relegated from the Premier League and if you want to run your club sensibly then you always have to keep an eye on the balance sheet.
"The No1 aim is to stay in business closely followed by winning promotion. You can look down the Football League and see plenty of clubs who have had financial problems."
While some fans believe Pardew is the wrong man to deliver in such circumstances, there are others who are prepared to give him more time.
George Noble, from the Charlton Supporters' Club, said: "What's the point in sacking the man when his hands have been tied? We will just have to start all over again.
"We would obviously be pleased to be doing better than we are but also realistic to know it takes time."
Tonight's opponents, Crystal Palace, failed to make the most of their two years of Premier League parachute payments following relegation three years ago.
Former manager Peter Taylor paid the price and, although his successor Neil Warnock led them to the play-offs last year, they have had a slow start to this campaign.
Palace will be without strikers Alan Lee and James Scowcroft, both have hamstring strains, and Calvin Andrew (knee).
