Newcastle opened their title defence with a 4-1 win in the third round last night with doubles from Joelinton and Will Osula doing the job for the Toon.
Howe said: "We want to win whatever is put in front of us and the attitude stems from us, the coaches and it should filter down.
"There is no difference between the games; these are opportunities to win trophies, and you can't just turn them away.
"So the hard rounds are the early ones. They are very difficult. Last year, we had to battle through against Wimbledon on the way to winning it; Bradford was the same. The mentality you can't switch off."
On fielding an experienced line-up, Howe also stated: "We wanted to win and wanted to score and try to entertain everybody that came.
"I thought we did that, it was always going to be a difficult game, nobody wants to make anything easy for you.
"Bradford are top of their league and we needed a bit of patience in our performance but once we got into our groove we were very good."