The Yorkshire side's striker Jermaine Beckford scored the game's only goal after 11 minutes at The Valley, firing past Charlton's debutant goalkeeper David Button from eight yards for his 16th FA Cup goal in his last 16 games.
Charlton's Dorian Dervite then deservedly got his marching orders after 57 minutes when the defender tripped Beckford as the Huddersfield man ran through on goal.
The victory ended a 10-game winless run for Simon Grayson's men and came on the back of their 6-1 league defeat to Leicester.
"The Championship is an unforgiving league and we were kicked up the backside," Miller said.
"We had a full and frank discussion after that defeat and we played as a team. There were some good individual performances but it was about the team performance. Although I did think Charlton kicked on with 10 men and we just tried to defend."
Miller praised match-winner Beckford for his goal.
"Jermaine can score goals. He's a natural goalscorer. I knew him from his time at Leeds and when he's smiling and happy, he's a threat," Miller added.
"Lately, he's just not had enough games due to injuries. But if you can get him and James Vaughan on the pitch they are a potent threat. The best in the Championship? I don't know.
"There's lots of teams spending mega money but they will certainly do for Huddersfield. They will both score goals."