The Cherries ran out 3-1 winners at Brunton Park to set up a third-round clash with Premier League Wigan and Howe was quick to credit the die-hard supporters who made one of the longest trips in English football.
"To take that many supporters to Cumbria was just incredible, the support they gave the lads throughout was fantastic and they made a huge difference," he told the club's official website.
"It's so important to everyone that we are in the third round, especially the supporters. They were magnificent at Carlisle and fully deserve to have a day out at a Premier League ground.
"I'm very pleased that they were rewarded with the win, and although it's yet another long journey for the next round, I can guarantee they will be there in large numbers."
Howe is yet to taste defeat in the 11 games since returning to the south coast and he could make it 12 with victory at Scunthorpe, another long trip, on Saturday.