Yannick Sagbo's equaliser helped the Tigers rescue a late draw against Championship outfit Brighton at the Amex Stadium on Monday night.
However, the draw did nothing to help Hull's congested schedule as they must first travel to Cardiff in the Premier League this weekend before resuming battle with the Seagulls at the KC Stadium next Monday for the right to host Sunderland in the quarter-finals.
With the club's only trip to Wembley coming in 2008 when they beat Bristol City in the Championship play-off final, Bruce admits he is likely to field another strong side.
"Once you get to this stage, then a quarter-final or semi-final are big days," he told the Hull Daily Mail.
"Not just for your manager but for supporters too. Why not? We might never get the chance. We've only been to Wembley once in 110 years, so why not?"