The Addicks had taken a third-minute lead at the DW through Marvin Sordell, and almost doubled their advantage when Reza Ghoochannejhad hit the bar midway through the first half.
However, Wigan showed signs of finding their feet just before the break when Callum McManaman hit the bar - and the second period was all one-way traffic.
Nicky Maynard had an 'equaliser' disallowed with seconds of the restart for offside, with replays apparently showing he was onside.
But it took until the 89th minute for Latics to level, when substitutes Josh McEachran and Marc-Antoine Fortune combined to devastating effect.
McEachran, making his debut after joining on loan from Chelsea, dissected the defence with a delightful through ball that was expertly finished by Fortune.
And then fellow substitute Jordi Gomez won it for Wigan on the stroke of full-time with a marvellous free-kick from 25 yards.
"It's tough to take," admitted Powell. "It was such a brave performance, we put our bodies on the line.
"Being 1-0 up for so long, and having put in a performance that was so committed and diligent, it looked like it was going to be our day.
"When it gets to that stage of the game, you're looking to just see it out.
"Sadly it wasn't to be. And it's the way it's going for us at the moment.
"It hurts. My dressing room is hurting, and so are the supporters.
"But we've got to remain steadfast and we've got to remain together, because that is the only way forward."
It was something of a patched-up side that Powell put out, something that made their resolute showing even more admirable.
"It was a side that we put together at short notice, with several products of the academy and two players making their debuts," the Charlton boss added.
"Obviously we lost two players during the transfer window, another one to suspension, and I also needed to freshen things up.
"We worked on our tactics and we were going well for most of the game.
"Even though Wigan had good possession, we still had some good chances to score more goals.
"Reza had an outstanding chance that beat the goalkeeper and hit the bar.
"You're looking for that to go in, and unfortunately for us it didn't.
"I can't fault any of the lads. Coming to a difficult place like this, an ex-Premier League side, with plenty of Premier League quality, it's not easy.
"I thought my lads acquitted themselves well, considering the amount of players who had never played in the Championship before.
"But it's got to be right to the end. And I hope all of them learn from the experience."
Wigan boss Uwe Rosler was frustrated with his side's profligacy in front of goal, with only seven of their 28 chances being on target.
But he was left to bask in the glory of an inspired trio of substitutions, who all made a critical contribution to the result.
"I remember not so long ago at Brentford, against Colchester, I took off Adam Forshaw - probably our best player - and the crowd was chanting 'you don't know what you're doing'," said Rosler.
"I brought three players on - two of them scored and the other made a goal.
"Sometimes you need a bit of luck, and we got that with the substitutions."
Rosler also felt his side deserved their break for continuing to play football and not resorting to 'route one' in search of a lifeline.
"I didn't want to go long," the German added.
"The temptation is to do that, and we don't have the players to do that.
"For me, the only way we were going to come back into the game was by playing football, and that's the reason I made the changes I did."