Liam Feeney and Chris Wood both failed to hit the target with good opportunities in a first half dominated by the hosts.
Substitute Dany N'Guessan came closest to opening the deadlock after the break with a close-range header that was cleared off the line by Chris Solly, but a resolute Addicks defence ensured the points were shared.
The result meant Chris Powell's men were undefeated in six games, while the Lions extended their unbeaten run to 13 matches.
In front of a sell-out crowd, the home side started brightly, with Feeney trying his luck with a driving run and shot in the opening minute.
Yann Kermorgant then flicked the ball into the path of Rob Hulse, whose shot was blocked by Josh Wright after 10 minutes, as both teams looked to break the deadlock in a hectic opening period.
Hulse's left-footed volley from a narrow angle flashed wide after 27 minutes, before Feeney spurned a great chance to give the hosts the lead.
Andy Keogh, playing with a broken toe, whipped in a great ball to the back post, but Feeney was unable to make a clean contact on the stretch, having got in front of a dozing Dan Seaborne, as his effort bobbled just wide.
Kenny Jackett's men began to impose themselves on the game, and made another good opening minutes later, but Wood's weak close-range effort failed to trouble Ben Hamer in the Addicks' goal.
Six minutes before the interval, Dorian Dervite's headed clearance fell to the feet of former Charlton trainee Wright, who struck a speculative 25-yard volley which looped over the bar.
The Lions continued to build pressure, and Nadjim Abdou was unlucky not to give the hosts the half-time advantage after unleashing a right-footed strike which flew wide.
Jackett then replaced the stunted Feeney with former Addicks loanee N'Guessan midway through the second half.
The change injected life back into the home side, as Keogh forced Hamer into a fingertip save with a stinging drive on the counter-attack.
Wright's 76th-minute corner then presented N'Guessan with the best opportunity of the half, but Solly kept out the substitute's free header.
Powell introduced Bradley Wright-Phillips nine minutes from time to increase the visitors' attacking threat, but the game ended in stalemate.