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Hartlepool manager Neale Cooper felt an error from Neil Austin gifted Charlton the corner from which they got their first goal in a 3-2 win.
Pools led at the break thanks to Peter Hartley's opener before the champions got back on level terms in the 70th minute through Danny Hollands.
Substitute Danny Haynes put the Addicks in front with a 78th-minute header and Yann Kermorgant extended their advantage three minutes later with a fine finish from an acute angle, before Gary Liddle set up a grandstand finish.
"I knew it would be a really difficult game," said Cooper. "They are a good side and that showed in the second half but we played a lot of good stuff.
"We played really well, pressed and played a hard game. We closed them down very well in the first half but it was a tiring game and I thought that caught up with us in the second half.
"But saying that, it was a little mistake that gave away the first goal. Neil Austin has got control of the ball, he has tried to pass it back, they get a corner from it when he could have easily played it away."