The Addicks – reduced to 10 players after Grace Coombs was dismissed just after the hour mark for denying Nikita Whinnett a goalscoring opportunity – thought they had snatched the win when Charley Clifford headed in from a corner in the 87th minute.
Amelia Hazard squeezed home from close range to ensure the points were shared.
Charlton went close on a few occasions in the first half, Sarah Quantrill denied Charlie Devlin when she was clean through and Ellie Wilson scrambled to make a vital challenge on Charlie Estcourt.
Whinnett and Devlin both saw penalty claims waved away by the official – the latter’s chip before she fell cleared keeper Georgia Robert but was cleared before the ball crossed the line.
Clifford said: “It was a frustrating end to the game for us, especially after going down to 10 and then scoring.
“Going into next week we need to keep believing that the win is going to come.
“We played well and were the better team but towards the end we showed a bit of inexperience, we couldn’t keep our heads straight.
“As a team we have 14 new players, so we need time to gel. Things haven’t quite dropped for us. Performances have been good, it’s just a case of that final-third end product.”
Charlton are bottom of the table but have a match in hand of Leicester City and Coventry United, the two clubs immediately above them.
Crystal Palace Ladies are seventh and lost 2-0 at Blackburn.
A well-taken first-half finish from Serena Fletcher put the hosts ahead before a late piledriver from Natasha Flint.
Aoife Hurley struck the post for the Eagles before the deadlock was broken.
Palace striker Bianca Baptiste said: ”We created a number of chances, but unfortunately we couldn’t finish them off and this is what happens.
“We’ve just got to get back in training again now this week and look ahead to the game against Charlton. At least that won’t be as much travelling for us.
“We’ve just got to go back to the drawing board. We’ll work hard on picking ourselves up and sort out what we need to come out on top against Charlton.”
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PICTURE BY KEITH GILLARD