Saturday's defeat to North End prevented Blues from settling the issue before the drama of the final day, but Fahey, who looked to have put the midlands club on their way to the top flight with the opener at St Andrew's, is adamant they have still got what it takes to finish the job.
"We can definitely bounce back," he told the club's official website. "Of course everyone was down after Saturday because that was our chance to do it in front of the home fans.
"Now we've got to do it the hard way but it's definitely not gone. If we win we're up. There is still a good spirit among the squad and we will be trying our best to get the result that we need on Sunday."
Birmingham will be promoted if they win, but if they draw and the Blades win then the Yorkshire outfit will go up. Defeat will consign Alex McLeish's side to a play-off place.