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Charlton are now three games without a win in League 1 after being held by Bury on Saturday.
The Addicks trailed to Jermaine Beckford's early opener in the first half but levelled through Josh Magennis.
However, the home side, despite having plenty of possession after the break were unable to find a winner and were left frustrated at the final whistle.
Charlton were without the suspended Ricky Holmes, who served a one-match ban having picked up five bookings in his previous five matches.
For the first half-hour they missed their most creative player. Too many times they found themselves chasing Bury who, despite a five-man defence, put plenty of players into forward positions.
Their early intent was rewarded inside nine minutes when Josh Laurent found Beckford, who produced a sweet 20-yard right-foot curler beyond keeper Ben Amos.
The home fans started to get restless but Karl Robinson's side showed their character before half-time.
Karlan Ahearne-Grant's lob went over the bar as well as keeper Joe Murphy, who was then down well to save from Magennis.
At the other end it needed a full-length save by Amos to turn behind Chris Maguire's long-range shot.
Charlton got themselves back into the game on 39 minutes when Jake Forster-Caskey's deep cross was nodded in by Magennis.
Had Ahearne-Grant's long-range shot been deflected the other side of the post, they would have gone into the break ahead.
That tone continued after the break with Charlton dominating possession. While Bury remained a threat through the experienced Beckford, they had to soak up plenty of Charlton pressure.
Murphy nearly handed Charlton the lead on the plate just after the hour when his pass sold Chris Humphrey short. Magennis got there first but, instead of shooting, he tried to play in Fosu and Murphy was out smartly to save.
It was Forster-Caskey's forward runs that caused Bury most problems and he almost came up trumps 13 minutes from time, meeting Jay Dasilva's cross but finding Murphy with his close-range header.
Charlton, though, did not create enough chances with substitutes Ezri Konsa and Joe Dodoo failing to make an impact.
Magennis nearly headed in an injury-time winner but his effort, from Chris Solly's cross, was turned behind by keeper Murphy.
Charlton: Amos, Kashi, Bauer, Pearce, Magennis, Clarke (Dodoo 78mins), Fosu, Ahearne-Grant (Konsa 64mins), Forster-Caskey, Solly, Dasilva. Subs not used: Phillips, Jackson, Konsa, Aribo, Sarr, Hackett-Fairchild.
Bury: Murphy, Leigh, Maguire (Dobra 67mins), Beckford, Reilly (Danns 56mins), Edwards, Aldred, Humphrey, Laurent, Cameron (Whitmore 18mins), Smith. Subs not used: Fasan, Williams, Bunn, Lowe.
Attendance: 9,895 (346 away fans).