It was the first win of the campaign for Howe's side against the League Two leaders, after goals from Max Gradel and Marc Wilson secured a third round tie at home to Preston North End.
Howe was pleased the team's application on a competitive night at the Globe Arena and acknowledged the travelling support for making the mammoth trip north.
"It was really important tonight," he told BBC Radio Solent.
"You need to win to get that winning feeling, we knew it would be tough on their own patch and the position they're in.
"Fair play to the players for their reaction to the equaliser. They showed great character to get a grip on the game again, we had a few chances weren't clinical the way they came.
"Moments like this can be the starting point for a season, it has given us a good platform.
"Overall I'm pleased with the attitude of everyone, they owed it to everyone connected with the club, not least the supporters who made the long journey."
Wilson's first goal for the Cherries gave the team the victory, as the centre-half rifled in a sumptuous effort from 25-yards.
Howe was surprised to see the Ireland international score from that distance but believed the result could have been greater following the 29-year-old's wonderful effort.
"It was a great strike," Howe continued.
"I didn't expect him to score from that range and I was pleased to see it nestle into the corner.
"It could have been much more though, we had gilt-edged chances in the first half and found it more difficult to open them up in the second. But it's a win and it's good to get that winning feeling."