Chris Dagnall was on target 20 minutes from time to send the Tykes through to the last 16 and allow the Tigers to concentrate on trying to clinch promotion from the Championship.
Hull manager Bruce said: "We have 18 games left in the Championship now without any distractions but it's always disappointing to go out of the Cup.
"If you get a favourable draw, before you know it you can be in with a chance.
"In the first half I thought we played well enough but unfortunately missed two or three really good chances and that's been our Achilles heel.
"We had several opportunities and Barnsley just had the one - but they took it."