Rovers beat Arsenal in the cup competition on Saturday to advance to the sixth round but struggled to find their feet against the Tigers at the KC Stadium.
Appleton said: "After the euphoria of Saturday there was always a danger of the players being unable to pick themselves up and repeat the type of performance they showed.
"You've got to give credit to Hull. They started the game okay and they certainly came out of the blocks second half really well."
Blackburn are currently 10th in the Championship on 44 points, seven points adrift of the playoff places.