Per Mertesacker and the impressive Alexis Sanchez scored the goals as the holders claimed a third round triumph at Emirates Stadium in a re-run of last May's final.
Hull centre-back Curtis Davies was the only player retained from the 2-0 New Year's Day win over Everton - a triumph that came at a signifiant price.
Before kick-off, City confirmed that defenders Andrew Robertson (ankle ligaments) and Liam Rosenior (hamstring tendon) are set for lengthy absences, along with midfielder Gaston Ramirez (adductor), with all injuries sustained against Roberto Martinez's side.
Rosenior will be out of 10 to 12 weeks, with Robertson and Ramirez facing four to six weeks on the sidelines.
Bruce highlighted these problems as a reason for his team selection and insisted the changes were not intended to play down the importance of the FA Cup to his club.
"We made 10 changes with all the injuries we have got, and that wasn't a case of disrespecting the cup because we had one of the best days of our lives in the competition last year," he said.
"It was always going to be difficult once we picked them [Arsenal] out of the hat."
Bruce conceded that Hull lacked quality in attack on Sunday and expressed a tentative interest in securing the services of Jermain Defoe on loan - the former England striker who is currently plying his trade in the MLS for Toronto FC.
"If we're going to be honest Arsenal deserved to win," he told the BBC. "Unfortunately, up the top end of the pitch we were unable to create anything.
"The disappointing thing for me is that the first goal is the first we've conceded from a corner. We should be doing better than that.
"We battled on valiantly but we weren't quite good enough."
Addressing the Defoe link at his post-match press conference, Bruce added: "He [Defoe] might be too expensive. If there is a chance we would be interested in him.
"But I don't want to get the hopes up of all the Hull supporters. There is a long way to go."
