Goals from James Dayton and Paul Heffernan were not enough to counter a Leigh Griffiths hat-trick and a shot on target from Matt Done, as Hibs denied Kilmarnock a Scottish Cup semi-final spot.
Evidently disappointed, Shiels said: "We have performed remarkably well this last while but you have to give Leigh Griffiths a lot of credit, you can't overlook that.
"But the basic defending of long balls was really, really poor and that was the key.
"We looked the team that was trying to play with invention and creativity but if you can't defend straight balls like that...they must have thought they had won the lottery. It was unbelievable, really poor."