Two goals in as many second-half minutes from Ryan Flynn and John Brayford were the difference at Bramall Lane, with that double salvo coming shortly after Charlton's Callum Harriott had wasted a golden opportunity to open the scoring.
The defeat denied Charlton a first Cup semi-final appearance since 1947, but Powell is now concentrating solely on his side's Championship struggles.
Charlton lie rock bottom of the division - four points adrift of safety, albeit with as many as four games in hand on some of their rivals - and Powell knows the club can ill afford to drop back into the third tier.
"We're disappointed with today but we have to move on," he told the club's official website.
"We have a few games in hand and it it is all in our own hands.
"I'm really disappointed for the fans because their support was brilliant and sadly, we couldn't give them what they wanted.
"You have to take your chances and we have had a guilt-edged one just before they scored."
