Albion achieved their only Premiership away win of the season at The Valley last season when Robert Earnshaw scored a hat trick in a 4-1 win.
Earnshaw is now on his way to Norwich in a £3.5million deal before the transfer deadline, and his absence was obvious as Albion failed to create too many chances, especially in the second half when Charlton dominated the game.
It was an even match in the first 45 minutes with both sides creating chances.
But Charlton's Darren Bent twice went close for the home side, firstly shooting wide after his pace had taken him past the Albion defence and then testing goalkeeper Tomasz Kuszczak, who had to save well after Bent cut in from the wing after picking up a rebound of the ball off of the corner flag.
Albion twice tested Charlton goalkeeper Thomas Myhre, the Norwegian international firstly turning Jonathan Greening's shot for a corner and then being lucky to deflect Geoff Horsfield's close-range header on to the post before it was scrambled away.
In the second half Albion failed to have a strike on goal as they were pushed back by Charlton, but the home side were unable to break down the visitors' solid defence.
Kuszczak did well to turn away Bryan Hughes' shot and from the resulting corner the Charlton midfielder headed wide.
Kuszczak was on hand again to save well from Darren Ambrose and Alexei Smertin, who has yet to score for Charlton, saw his goalbound shot deflected for a corner.
Charlton were persistently caught offside as Albion kept their cool and defended well to resist the pressure from the home side.