Alan Pardew's in-form Addicks made it 11 points from a possible 15 as they continued their recent revival.
It was a battling performance by Pardew's players who at times rode their luck, especially in the opening half.
From City's perspective it was another point gained in their own battle to beat the drop.
However, manager Stuart Pearce will view it as two dropped as they ought to have registered their first home league win since New Year's Day.
City at least halted a depressing run of four successive league defeats at Eastlands, although it was hardly a convincing display. However, wins at Middlesbrough and Newcastle in their two previous league games provided some respite in their battle for survival.
City completely dominated the opening half but were unable to find a route to goal.
The in-form Emile Mpenza, who had scored in each of City's last two games, could easily have scored a hat-trick in the opening 16 minutes.
The Belgium international had one effort saved by keeper Scott Carson, another headed off the goal-line by Amady Faye, before having a goal-bound shot blocked.
Joey Barton twice and Stephen Ireland also had decent attempts on goal as City did everything but find the net, Barton bringing a fine save out of Carson.
Charlton had a goal from Talal El Karkouri chalked off for a clear offside while their best chance of the opening period came when City defender Richard Dunne almost headed into his own goal when he tried to cut out a cross from Jerome Thomas.
City failed to build on their first-half promise as the second period became a disappointing spectacle.
Nedum Onuoha, again deputising for the injured Micah Richards, ought to have broken the stalemate on the hour but his free header flew high over the crossbar.
Charlton's Chinese international Zhi Zheng had his side's best chance of the game in the 73rd minute but Onuoha blocked his shot which went harmlessly wide.
City brought on Georgios Samaras and Trevor Sinclair for the last 16 minutes as they looked for new ways of conjuring a match-winning goal.
The double substitution failed to improve City's fortunes as they failed to find the net for a 17th time in 36 competitive fixtures this season, which is one of the key reasons why they have found themselves involved in a battle to avoid relegation.