Turner, who handed home debuts to seven of his nine summer signings, watched on as two first-half goals in quick succession from Deon Burton and Nicky Bailey secured the points for the Addicks.
The best chance Pools mustered came when Charlton goalkeeper Rob Elliot tipped an Antony Sweeney effort over the bar.
"You can see why they are among the favourites this season," said Turner. "You could see the difference in quality and confidence. We are not at that standard at this time.
"We had chances and strikes on goal, but they took their chances."