Fulham dominated possession but struggled to create many clear-cut chances
Fulham missed the chance to move within a point of an automatic promotion spot after being held by an out-of-form Charlton side.
Scott Parker's visitors had the better of the first half - Bobby Decordova-Reid forcing two decent saves from Dillon Phillips - while cries for a penalty were ignored after Alfie Doughty accidentally handballed in the box.
It was more even after the break, Fulham going closest to a winner when Michael Hector headed wide when unmarked from a corner at the back post.
Charlton had just one shot on target, Josh Cullen's near-post effort kept out by Marek Rodak, though sub Jonny Williams was denied a late tap-in by Cyrus Christie's vital block.
The draw leaves Fulham third in the Championship - three points behind second-placed Leeds having played a game more - though they remain above Nottingham Forest, who drew with Reading.
Meanwhile the Addicks stay 19th, six points clear of the drop, having won just one of their past 17 league games.
The Cottagers badly missed the attacking threat of injured duo Anthony Knockaert and Aleksandar Mitrovic, while Charlton could not capitalise on a lively atmosphere at The Valley after boss Lee Bowyer signed a new deal earlier on Wednesday.
Charlton manager Lee Bowyer told BBC Radio London:
"It was a decent point against a very good Fulham side.
"From the start minute to the last my players were excellent - no switching off, young lads tracking and we were excellent defensively.
"We had to hit them on the break at times but, come on, we're playing against a Premier League side there and I thought we deserved a point."
Fulham boss Scott Parker told BBC Radio London:
"It was always going to be down to that one big chance that you needed to take, and then it's a 1-0 win, dust yourselves down and get out.
"We probably had two big chances that we didn't take, and from there it's probably fair to say if you can't win it, you don't lose it.
"Overall I'm a little disappointed but I think when all is said and done this will be a decent point on the board."