The Addicks started brightly and were nearly ahead in the 19th minute, but Bradley Wright-Phillips saw his effort well saved by Ben Amos.
Sone Aluko could have put the visitors in the lead before the break but his weak effort was easily blocked by Ben Hamer as a fairly uneventful first period ended in a stalemate.
Hamer's form was clear for the Hull players to see as he produced a superb stop to keep Nick Proschwitz's long-range effort out.
Robert Koren had an unusually quiet game but the playmaker nearly put Hull ahead with a curling effort that sailed just wide of the Charlton goal.
Despite Hull being the better side in the second period, the hosts nearly stole a victory in the final minute. However, Johnnie Jackson's strike was well saved by Amos.