Dailly saw red for violent conduct but Addicks keeper John Sullivan made a string of impressive saves to deny Oldham victory.
Oldham's Chris Taylor went close with an early free-kick and Sullivan had to be alert on 13 minutes to save from Aidan White.
Bradley Wright-Phillips shot wide as Charlton began to threaten, but the visitors missed a clear chance just after the half-hour when Therry Racon was denied by Dean Brill in a one-on-one with the keeper.
Charlton went down to 10 men after 34 minutes, Dailly receiving a straight red card when he lashed out in retaliation to Reuben Reid's foul. Oldham piled on the pressure but Ritchie Jones headed over and Sullivan pulled off two flying saves from Cedric Evina.
Charlton's Jon Fortune cleared another effort off the line before the Oldham frustration was summed up when Jean Yves Mvoto wasted a chance from six yards.