Chris Kirkland was unfortunate to have been on the losing side, after replacing the out-of-form Jerzy Dudek.
Emile Heskey, who passed a late fitness test, limped off the field soon after the first goal, and was replaced by John Arne Riise.
Despite second half pressure, including a disallowed goal for offside, Liverpool were unable to equalise and were punished when Konchesky doubled the lead 13 minutes from time.
The defeat puts Liverpool back to fourth in the Premiership behind Arsenal, Chelsea and Manchester United.
Charlton: Kiely, Rowett, Rufus, Fish, Powell, Lisbie, Parker, Kishishev, Konchesky, Euell, Bartlett. Subs: Roberts, Jensen, Young, Svensson, Fortune.
Liverpool: Kirkland, Traore, Henchoz, Hyypia, Carragher, Murphy, Hamann, Gerrard, Heskey, Owen, Diouf. Subs: Dudek, Baros, Smicer, Riise, Diao.