Bruce is unapologetic about prioritising survival in the Barclays Premier League and has put out second string sides so far in the cup, making 11 changes against Leyton Orient and nine more for Tuesday night's 1-0 win over Huddersfield.
The Tigers have never made it as far as the quarter-finals of the competition and although the prospect of breaking new ground might appeal to fans, Bruce is keeping fully focused on the main job this year.
"I've picked a team that got through against Orient - who are doing all right, they're unbeaten (in the league) - and I've picked a team that has got through against Huddersfield so I'll continue along that way," said Bruce.
"I'm not going to be sidetracked trying to get a cup run. It's very nice to have a cup run but my priority is to keep this club in the Premier League.
"Chester is out for six to eight weeks, Koren the same, and if we add one or two more to that we're in trouble.
"We don't have the strength in depth yet."
One of the major positives from Hull's low-key victory over the Terriers was a first goal of the season for striker Nick Proschwitz.
The German forward, a B£2.6million signing last summer, has found himself firmly out of favour this term and was even offered the chance to leave in the summer.
But he grabbed four goals in a reserve team match last week and finished emphatically when George Boyd's 59th-minute cross landed nicely for him.
Proschwitz is unlikely to leapfrog Danny Graham or Yannick Sagbo in the first team any time soon, but Bruce was glad to see him provide a trademark finish.
"Nick's confidence has never been in doubt, the one thing the kid can do is score," said Bruce.
"When the opportunity arises you expect him to score, that part is so easy for him.
"It's the other parts of his game that has to improve and we have to keep working with him.
"He's better than he was 12 months ago but he still has to adapt.
"He's part of our 25-man squad. I wanted him to go out but he didn't want to go.
"The more he plays and the more he scores, good for him."
Beaten Huddersfield manager Mark Robins defended his own decision to ring the changes, insisting games such as this are the only real chance to learn about his young players.
One, 18-year-old Duane Holmes, caught the eye with a wonderful cameo from the bench and that made the experiment worthwhile for Robins.
"I read a hell of a lot in the press about young English players not having the opportunity...well where do you give them a go if not here?," he said.
"There's no other opportunity like it. We had an average age of 23 and one or two of them might be stars of the future.
"Duane has got a little bit of something different. He's 18 and he has a bright future.
"He's definitely got something and he gave us a bit of hope towards the end."