The Blues boss said that he was "proud" of how his team bounced back from last weekend's 5-1 defeat to Leyton Orient with a shock win over the Championship outfit.
"We had a lot of kids out there and they were fantastic tonight. They showed no fear and should be proud of themselves," Sky Sports News quotes him as saying.
"It was a terrific game after Saturday, when we were poor (in a 5-1 loss at home to Leyton Orient), but that's what the Cup is all about. There were so many positives and I think we deserved our little bit of luck in the game.
"These lads are going to get better and this game was important for the club. We won a little bit of respect back."
Carlisle progressed to the competition on penalties following a 3-3 draw at Brunton Park.