Millwall manager Kenny Jackett bemoaned the lack of 'creative spark' as his side failed to turn dominant possession into maximum points at the New Den.
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The Lions stretched their unbeaten run to 14 matches, moving into fifth and keeping a fourth consecutive clean sheet.
Both sides had opportunities but Millwall will certainly consider theirs were better, former Addick Dany N'Guessan unfortunate to see his late goal-bound header stopped on the line by a well placed Chris Solly.
Chris Wood was Millwall's biggest threat while Andy Keogh was his perfect foil as the hosts piled on the pressure, particularly during a one-sided second half.
"I thought it was a dominant performance, barring the finishing," said Jackett.
"In the second half, I don't think Charlton got out of their half.
"I can't remember them having a shot, but it didn't quite drop for us in the box. Perhaps we needed a spark of creativity.
"I'm pleased with the players. A lot of our game was right and it gives me as a manager, good encouragement for the future."
Charlton manager Chris Powell had no complaints with the result, with defender Leon Cort a rock in the heart of their defence.
His team are now without a defeat in seven and haven't conceded in their last three trips away from The Valley.
"They stood up to the test and it's quite an intimidating place," he said.
"This place will test your resilience and bravery and my team was full of that, especially the centre backs and keeper.
"We didn't create much but we're playing against a side in good form. I thought we were competitive and it was a performance full of bravery.
"They're in a very good place under Kenny but as the game wore on, you could see it was a case of making sure we wouldn't be beaten.
"Whether we had that moment of quality to win the game is questionable, but I'm happy we've walked away with a point unbeaten.
"There were no winners today and no bragging rights for anyone in the office."
Meanwhile, Jackett hopes the return of injured players will them a vital boost for the remainder of the campaign.
"For me, if we can get some of our injured players back and available and keep somewhere near our best side and squad fit on a regular basis," he added.
"James Henry, Darius Henderson and Liam Trotter are all good players to come back and they will really strengthen us in the final third of the pitch.
"Going forward, I feel that we have more creative options than we've had for a while."