The Premier League outfit cruised to a 2-0 win over their Championship opponents at the Riverside Stadium on Saturday, courtesy of goals from Aaron McLean and Nick Proschwitz.
Strike duo McLean and Proschwitz were among nine changes to Hull's starting XI from their 2-0 defeat at Liverpool on New Year's Day after a sickness bug swept through the camp in recent days.
And manager Bruce was content with the professional manner in which his team secured their place in round four.
"Considering the problems we have had with illness, it was hard to put a team together and we made nine changes, but it turned out to be comfortable from the start - it turned out really well," said the former Sunderland boss.
"It just shows how far we have come in terms of the squad, and when you get in the Premier League that enables you to strengthen."
Bruce went on to admit that both McLean and Proschwitz could leave the club this month in search of regular first-team football, although he revealed that there are no imminent arrivals at the KC Stadium.
"Obviously that is a possibility (McLean and Proschwitz leaving), if an opportunity comes along and suits both players then that could happen," he added, before responding when asked about whether any signings were close to completion: "Not yet, but that is just starting."
