Following their 2-1 Champions League defeat by Benfica in Lisbon in midweek Hoops boss Neil Lennon had claimed fatigue was impacting on his squad and it looked that way as they never got going against the neat and tidy visitors.
Kris Commons and Mikael Lustig missed good chances for the home side in an otherwise dull first half but there was no second-half surge from the champions and indeed, after McKay notched in the 65th minute from close range, he later spurned a good chance to double their lead when he hit the bar with only Fraser Forster to beat.
Inverness manager Terry Butcher had challenged his side to maintain their record of having scored in every game this season and he will have no complaints although conversely, Lennon had a shouting match with one Celtic fan behind the dugout before the game had ended.
It was an afternoon of frustration for the former Hoops skipper who made three changes to his starting eleven.
Commons, Beram Kayal and Tony Watt were drafted in with Kelvin Wilson (flu), Joe Ledley (groin) and Scott Brown dropping out, the Hoops skipper shrugging off an on-going hip complaint which may require surgery to take his place on the bench
Butcher made one change to the side which lost 5-1 at home to Motherwell last week, with Philip Roberts in for Gavin Morrison.
The absence of the Green Brigade - the vociferous and occasionally controversial section of the Hoops support who were boycotting the match after claiming they had been subject to "oppressive police tactics" in recent months - deadened the atmosphere further in a half-filled stadium.
In the 12th minute the home fans who did turn up gave a standing ovation, apparently in support of the Green Brigade's actions, but that was mostly all they had to applaud in a lacklustre start to the match.
Caley defender Graeme Shinnie fired a 25-yard free-kick over the bar before Commons had an effort which failed to trouble Caley keeper Antonio Reguero.
The Highlanders' goal almost came under threat in the 17th minute when Kayal played in Lustig but his attempted cut-back from the byline to Gary Hooper was thwarted by a fine Josh Meekings tackle.
Almost 10 minutes later Celtic defender Charlie Mulgrew picked out Hooper with a cross which allowed the striker to set up Kayal at the edge of he box but the midfielder's shot was blocked by Caley skipper Richie Foran and the ball spun through to Reguero.
Moments later at the other end, Owain Tudur Jones set up Andrew Shinnie but his 20-yard drive limped wide of the target.
The champions then squandered two good chances to break the deadlock.
In the 39th minute, as the Parkhead side broke swiftly, Hooper sent Commons through but the Scotland midfielder's angled-shot from 12 yards was wayward.
Two minutes later Lustig had a similar and possibly better opportunity when Hooper cleverly allowed a Kayal pass to run through to the right-back but he hit the side-netting with his unconvincing effort.
Celtic began the second half as they ended the first, on the front foot, but with still several gears to find.
The visitors, resolute in defence, carried more than a hint of danger on the break.
Parkhead defender Efe Ambrose came to Celtic's rescue in the 54th minute when he cut out a dangerous cross from midfielder Aaron Doran and although the corner came to nothing it served to accentuate the sense of frustration inside Celtic Park.
Caley's goal was not a surprise and came through another swift counter.
Roberts took a pass from Doran inside the Celtic box, turned inside Adam Matthews and Mulgrew, and fired the ball across for McKay to guide the ball past Forster, with the home fans claiming offside.
Paddy McCourt replaced Watt and Brown came on for Matthews but before the second substitution there was another scare for the Hoops when Andrew Shinnie played in Tudur Jones but he could not set himself properly and his effort was easily saved by Forster.
Celtic, urged on by their fans, stepped up the pressure and Gary Warren hit his own post under pressure before Reguero made a good save from what looked to be a Samaras header.
At last the match was warming up and before Hooper was replaced by Lassad in the 75th minute, Lennon was warned by referee Calum Murray after his frustrations boiled over.
With nine minutes remaining and the Caley goal under siege, Reguero made a fine save from Commons powerful drive from 16 yards with the Hoops midfielder firing the rebound over the bar.
In the 83rd minute Caley should have scored the second when they broke in a two-versus-one situation.
Doran set up McKay who hit the bar with only Forster to beat before the Caley midfielder's shot from the rebound was cleared off the line by Ambrose.
The Highlanders were made to defend for the rest of the match but held on for the win, as Celtic Park echoed to the sound of boos at the final whistle.