The Blades sailed into a three-goal lead in the tie at Loftus Road on Tuesday night and despite a spirited fightback Rangers were knocked out of the competition losing 3-2 to their Championship rivals.
"The way we started the second half was a disaster," Hart said after the match.
"We've gone 15 games without a clean sheet and you can see why. That is a side of our game that has to improve.
"It was a very spirited comeback but it was too little, too late."