Jermaine Beckford scored the game's only goal after 11 minutes, and with Charlton defender Dorian Dervite sent off early in the second half, Powell's men struggled to create chances.
Powell, evidently furious at his side's elimination from the Cup, said: "To say I'm frustrated is the understatement of the year.
"I'm not enamoured with what happened today. I know we went down to ten men but we went out with a whimper.
"It was a poor goal for us to concede and it gave us a mountain to climb. I'm not happy with the way it has panned out.
"I put in a few players to give them a chance to show they're ready to play a part in our season and also it's the cup and I really wanted us to be in the fourth round.
"I know we didn't have as many fans as we usually do but we wanted to perform. Huddersfield are on a bad run but we really didn't get a foothold in the game.
"We showed last week at Watford what we can do when we get in good positions and create chances, but we never really did that today. We've been okay away but not done enough in front of our fans. I want us to be better at that in 2013 and it starts next week at home to Blackpool."