Manuel Pascali grabbed the only goal of the game to inflict a first league loss of the season on the Scottish champions and prevent them from claiming a 15th consecutive victory on the road.
Rangers had enjoyed a 12-point lead over their Old Firm rivals heading into last weekend’s action but a goalless draw against St Johnstone and the 1-0 reverse against Kilmarnock – combined with three wins for Celtic – means the Hoops have closed the gap dramatically.
McCoist said: “I don’t see it affecting the confidence of the players. We’ve lost our first league game today and it’s disappointing. We’ll have a look at the reasons for it. There certainly won’t be any panicking.
“We were disappointing against St Johnstone as well and today was the same. We will look at what we can do better.
“Contrary to what a lot of people maybe thought, I didn’t think we had won the title last week.
“I didn’t see us losing the game down here today. That wasn’t in the plan. We were 12 points clear but we knew there would be twists and turns to come in the championship. Nothing is handed out in November.
“It’s down to four points and I would rather they were in our favour than against us but I won’t lie to you, it is a little bit disappointing.”
Neil Lennon believes his Celtic side are finding top form just in time for their crucial Europa League clash with Atletico Madrid at Parkhead on Wednesday. The green half of Glasgow are in third place behind the Spanish club and Italian outfit Udinese with five points from four games but could go top of the table with a win.
The rejuvenated Hoops go into the penultimate Group I game with five straight wins following the 5-0 thrashing of St Mirren on Saturday.
Having watched striker Gary Hooper help himself to a hat-trick against the Pars, Lennon looked ahead to the Atletico clash.
“It is a game we can’t afford to lose. A draw might not be enough but if we win it, it puts us in a great position.
“We have picked up five wins in a row now and we are in good form. The players are in the habit of winning games and that will give the whole squad a shot in the arm.”
Much-maligned striker Georgios Samaras inspired Celtic after opening the scoring in the fourth minute when he capitalised on slack defending by the visitors.
And after Hooper had secured the match ball with three goals which exemplified his penalty box prowess, 18-year-old Dylan McGeouch, on for James Forrest, scored his first goal for the club in the 72nd minute with a wonderful solo effort.
KILMARNOCK: Bell, Fowler, Sissoko, Pascali, McKeown, Kelly, Buijs (Racchi 7), (Silva 75), Hay, Harkins, Shiels, Heffernan (Gros 90), .
RANGERS: McGregor, Broadfoot, Perry, Goian, Whittaker, Davis, McCulloch, Edu (Bedoya 70),Lafferty (Hemmings 40), Jelavic, Aluko (Fleck 85).
Referee: A Muir (Scotland).