Bradley Wright-Phillips put the hosts ahead in the 10th minute but United equalised just before the half-hour mark when Ben Marshall's drive took a deflection on its way past Addicks keeper Rob Elliot.
Carlisle capitalised on loose passing and a frustrated home crowd to take the lead in the 62nd minute through Craig Curran and the result was put beyond doubt by Rory Loy with 10 minutes remaining.
Powell said: "I don't think in those four games that confidence has dissolved. Maybe we got the rub of the green in our first four games, but after going one-nil up we then didn't perform to our capabilities.
"We've conceded poor goals at vital times, without a doubt. I've said before that in games like this one and Friday, you can't lose them. If you walk away with a point you can start again but they were cheap goals and considering the position we're in you'd expect us to be buoyant but we didn't have the confidence to push on."
He added: "We need to be brave and stick together and be the team I know we can be, but it's going to take a bit of talking on the training pitch. Roll on Saturday because the only way to amend it is on the pitch."
Source: PA
Source: PA