A keenly-fought quarter-final encounter at Bramall Lane saw few opportunities of note created before the hour mark, with neither side willing to open up with a day out at Wembley on the line.
It was, however, to be the Addicks who got the first clear sight of goal - with Callum Harriott sliding wide of a gaping target following a quick free-kick which allowed Marcus Tudgay to loop the ball over Blades keeper Mark Howard.
He was made to pay on 65 minutes as the hosts broke the deadlock through Ryan Flynn and added a second moments later as Richard Wood deflected a John Brayford strike past a wrong-footed Ben Hamer.
Powell admitted afterwards that Harriott's miss proved to be a turning point in the tie, with Charlton unable to give their 5,000 travelling supporters anything to shout about.
He said on the club's official website: "Goals change games.
"You have to take your chances and we had a gilt-edged one that we put past the post before they went up the other end and nicked a goal.
"It was unfortunate for Callum because he was lively and played well, but if you're a goal ahead then you've got something to hang on to.
"If we go ahead then the game can become stretched, as it did when we started chasing it, so that was a big moment for us.
"There weren't too many moments but that was definitely one that could have put us in a position to win the game.
"I'm really disappointed for the fans because their support was brilliant, a lot of them came up overnight and sadly we couldn't give them what they wanted."
Charlton must now turn their attention back to the scrap for Championship survival, with Saturday's results having dropped them to the foot of the second tier table, four points adrift of safety.
Powell, whose side have four games in hand on many of the sides above them, added: "It can't be anything else now.
"We're disappointed with today but we move on. We have a few games in hand and it's all in our hands.
"If we win both of the next week's games (against Huddersfield Town and Millwall) then the table will have a different complexion."