SO much then for Fortress Parkhead.

Barcelona may have been unable to withstand the ferocity of Celtic on their own patch, but domestically it is an altogether different story. Inverness Caledonian Thistle yesterday became the latest Clydesdale Bank Premier League team to have their way in the East End of Glasgow, a solitary second-half goal from Billy McKay meaning the Parkhead club have won just half of their SPL matches and taken just one of the last nine points available at Parkhead.

In total, 17 league points have now been dropped before November is out, compared to 21 for the whole of last season. There has been a blithe assumption that such form will correct itself eventually, but this trend must be worrying for the club's supporters.

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The distance of six points now separates eight teams, including fifth-placed Inverness. For all Celtic's failings – they looked jaded throughout their 25th match of the season in all competitions – it is worth dwelling upon the achievement of the Highland side. This was their first league victory at this ground, and completes an enviable double after their dismantling of Rangers in the Scottish Communities League Cup on Hallowe'en. McKay's goal was the 28th they have scored in the league this season, more than any other club.

No wonder Terry Butcher had a smile on his face as he looked ahead to returning north via a stop at a pub and a fish and chip shop in Auchterarder. The match might not have altered Butcher's opinion that Celtic will be champions, but he did feel emboldened to take issue with chairman Kenny Cameron on the subject of league reconstruction, which sees SPL teams planning two leagues of 12, which changes to three mini leagues of eight.

Quite simply, Butcher thinks the league should stay the way it is. "I have seen the proposals and I'm not happy with them," he said. "The way the SPL is going, everybody can beat everybody else, it's just a great league."

Frustration was the main emotion for Celtic yesterday. Neil Lennon made three changes from the side which went down in Lisbon and so uninspired were many of the performances that he should have made more.

The Northern Irishman had to be spoken to by referee Calum Murray as he remonstrated about a free-kick awarded against substitute Paddy McCourt and took an altercation with a couple of his own supporters so personally he spoke afterwards about quitting the club.

Even the arrival from the bench of captain Scott Brown, as he bravely soldiers on ahead of scheduled hip operation, was unable to save his team. Afterwards he said the home form was becoming a concern, but defended his players' application amid accusations they were too preoccupied with the forthcoming Champions League decider against Benfica.

"One point out of nine is not good enough," he said. "If players are thinking that way, it is a lack of professionalism, but I can't make that accusation against any player because I am not aware of it."

One exception from the general Celtic malaise was Beram Kayal, and he was prominent as Celtic spurned the only two genuine chances of a sleepy first half. Gary Hooper fed Kris Commons, who finished wildly then Mikael Lustig ran on to some excellent play from the Israeli, only to find the sidenetting.

The match changed just after the hour mark, however, when Aaron Doran burst forward and fed Philip Roberts down the right. The Arsenal loanee fooled Adam Matthews and Charlie Mulgrew with a cute drag back and his low centre was tucked in by McKay.

The closest Celtic came to a riposte was when Antonio Reguero saved from Commons and when the post spared Gary Warren's blushes from a dangerous low cross, but it was Inverness who almost doubled their advantage.

Doran fed McKay on a quick counter, and hit shot struck the underside of the crossbar, with only the fleet-footed Efe Ambrose denying Doran a tap-in from the rebound.

Fortunately for Inverness, the final whistle arrived to prevent the Irishman having to confront his manager. "I think we would have left one passenger behind" said Butcher. "Mr Doran would have had to find his own way home."