Substitute Nuno Capucho was the visitors’ unlikely hero when he headed home a Mikel Arteta free kick to put his side 3-2 up with just four minutes remaining. But he did so from such close range that Jefferies felt his goalkeeper should have got there first.
He said: “Nobody should be scoring from a header a yard out. You are either looking for your defenders to be out there or you are looking for your goalkeeper to come and take it.
“I was pretty angry that we lost a goal from a header in the six-yard box. The goalie made a couple of good saves today, but I felt if he had come for that we would have got a point out of the game.”
The result cut Celtic’s lead at the top back to five points, and Rangers manager Alex McLeish was delighted to have avoided dropping two more points away from home.
Shota Arveladze supplied Rangers’ two other goals, with Gary McDonald cancelling out the first in the first half and Peter Canero then firing Killie ahead just after the break.
McLeish was also convinced Peter Lovenkrands should have been awarded a first-half penalty when brought down by Gordon Greer.
He said: “It was a barge in the back. Anywhere else on the field, it would have been a free kick no question.
“The guy would probably have been sent off, so maybe that was the dilemma for the referee, but there was no way the centre-back was going to get near Lovenkrands.
KILMARNOCK: Dubourdeau, Shields, Greer, Dindeleux, Hay, Canero, Fulton (McLaughlin 89), McDonald, Murray (Hardie 71), Boyd (McSwegan 35), Nish.
RANGERS: Klos, Ricksen, Berg, Ball, Emerson (Capucho 80), Arteta, Hughes, Vanoli, Arveladze, Mols (Ostenstad 90), Lovenkrands.
Referee: J Underhill (Scotland).