The hosts should have gone in front in the seventh minute after Miguel Llera's pass put Bradley Wright-Phillips through.
The Addicks striker cleverly chipped Hartlepool goalkeeper Scott Flinders only to see his shot hit the woodwork.
Charlton debutant Callum Harriott volleyed just wide of the target, while Flinders did well to gather Llera's free-kick as the home side made a bright start, but the Addicks were unable to build on their early momentum and were forced to go in level at the interval after a scrappy end to the first half.
Flinders produced a fine stop within a minute of the restart, tipping over Wright-Phillips' 25 yard effort, but Hartlepool came close in the 54th minute as Sam Collins' stinging shot beat Rob Elliot and crashed against the crossbar, while Andy Monkhouse's shot was cleared off the goalline by Llera.
Charlton's Federico Bessone also hit the crossbar with a powerful shot from just inside the penalty area in the 79th minute, but that was as good as it got in a disappointing end of season finale.