Johnnie Jackson opened the scoring and Scott Wagstaff then hit a post with an angled drive which surely would have sealed Charlton's victory.
But Reda Johnson levelled before debutant Leroy Lita swept home Jermaine Johnson's cross from six yards out as Wednesday snatched an unlikely three points.
"That's football, sometimes you love the game and sometimes you hate it," said a shellshocked Powell, whose team missed the chance to climb to within five points of the play-offs.
"It's one of those days that hasn't gone for us. The turning point was when we hit the post, that would have sealed the deal for us.
"It's a tough way to lose after playing our part in a tough game. We got stronger and better as the game went on and went ahead through a good goal, but then couldn't see the game out
"It's a bitter pill to swallow but the players have done terrifically well this month."