Ten-man Charlton held on to secure a share of the points against Oldham.
Chris Taylor went close for the hosts with an early free-kick before the visitors threatened when Therry Racon was denied by keeper Dean Brill.
The Addicks were reduced to 10-men after 34 minutes when captain Christian Dailly lashed out in retaliation to Reuben Reid's foul.
Oldham piled on the pressure but John Sullivan pulled off two flying saves to deny Cedric Evina.
Oldham Athletic player-manager Paul Dickov told BBC Radio Manchester: "We a lot of possession, crosses and shots but just didn't have the killer instinct at the end.
"There were a lot of balls 'ping-ponging' in the box that didn't quite seem to fall for us but we have to be more ruthless.
"We've got five games left, we have to concentrate fully on what we've got here but we're out watching games and preparing for next season."
Charlton manager Chris Powell told BBC London 94.9:"I am disappointed. Especially in the circumstances that you come to a place like Oldham away and you want all 11 men on the pitch.
"There was an incident and I had to take a player off, a creative player in Therry Racon who had a very good chance to put us 1-0 up.
"Sadly due to circumstances out of his control I had to take him off. I think it shows the togetherness and work ethic of our players because they all dug in"