It was the London side's fifth goalless draw in their last eight Premiership games.
Manager Alan Curbishley has made no excuses for his team going "ugly" and they produced another strong defensive performance that lacked any cutting edge in attack.
With Wednesday's FA Cup sixth round replay against Middlesborough at The Riverside in his thoughts Curbishley rested 20-goal striker Darren Bent, who has been carrying a slight ankle knock, and was also without Luke Young, Bryan Hughes and Chris Powell.
With both clubs safely in the Premiership next season this mid-table clash gave them the chance to play without any pressure as they looked for a top 10 place - but there were few goalscoring opportunities in a disappointing match.
It took more than 20 minutes to produce a shot on target - Mikel Arteta's speculative cross being tipped over the bar by former Everton goalkeeper Thomas Myhre.
It got to injury-time before the match sprung into life, with Everton's James Beattie forcing Myhre into another tip over.
Charlton, in a spell of pressure before the break, tested the Everton defence, but with no end product.
Joseph Yobo put in a last-ditch tackle to deny Jason Euell and Richard Wright had to scramble back to clear Matt Holland's looping shot, which had initially deceived him.
After the break the game opened up a little, with Jay Bothroyd firing wide for Everton and James McFadden also missing the target.
Charlton made two changes just after the hour in a bid to become more attack-minded, and as they upped the pace Dennis Rommedahl saw his goalbound shot headed off the line by Alan Stubbs, and then had another effort deflected for a corner.
Marcus Bent almost won it for Charlton in injury-time against his former club, but his shot was comfortably saved by Wright.
Everton will be disappointed that they didn't make more of the fact that Charlton were not at full strength, but this was a predictable result from two sides whose performances this term have been almost identical.