Hill saw his side go ahead through Ricardo Vaz Te, but their lead lasted less than two minutes.
Swansea went on to take a 3-1 lead but, despite Vaz Te getting a second, failed to force a replay as the Swans eventually ran out 4-2 winners.
"Once we go one-nil up with the strategy we use we shouldn't be conceding that goal. Prior to that they didn't open us up too many times. We allowed the opposition to have the ball. It was very, very disappointing, but the players will be forgiven," said the 42-year-old manager.
"The time of the second goal really, really hurts and it hinders our opportunity to get anything out of the game because we know how good they are with the ball.
"Once they did take the lead there was only ever going to be one conclusion. The players are giving it everything, but they making mistakes that are costing us goals and games. It's harsh on players' performances to be judged on mistakes but that's what we do. We're all accountable for results. Mistakes are really hindering us and our progress."
Barnsley will be looking to bounce back when they travel to the Walkers Stadium to face Leicester next Saturday.