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 £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.