The resulting corner almost brought a goal for Genk, but Wilfred Ndidi headed over from close range after getting above his marker.
Genk continued to push for the game's opening goal during the first half, with Igor de Camargo slicing wide after Julien Gorius was denied by the legs of Henderson.
Johann Gudmundsson then forced a save from Genk goalkeeper Marco Bizot at the other end before the home side finally made their dominance count on 36 minutes as De Camargo nodded in following a cross from the left.
Charlton looked more confident at the start of the second half following 11 substitutions, but it was Genk who threatened first as Nick Pope was called into action to push away a header.
The Addicks saw more of the ball than their opponents for the remainder of the second half, though they were unable to turn their possession into clear-cut chances. The best that Charlton could muster was having an effort cleared off the line with four minutes left.