CELTIC losing to Ross County is no laughing matter.

While Derek Adams was discussing his side's victory over the best team in the country – not his first as County's manager – he was momentarily distracted by a nearby supporter laughing loudly with one of his friends in the main stand. The fan, doubtless fuelled by an afternoon's corporate hospitality and his team's stirring result, found himself on the sharp end of Adams's tongue. The manager barked at him to be quiet. Adams has such a grip on things at Global Energy Stadium that even supporters are brought to heel.

There were a few factors behind Celtic's defeat, their sixth in the Clydesdale Bank Premier League this season, and not least of them was a generally unimpressive and flat performance from Neil Lennon's team. After Juventus last midweek they didn't look up for an afternoon in the bitingly cold Highlands. Only because Michael Fraser, the County goalkeeper, flapped hopelessly at a Charlie Mulgrew corner and a shot from Gary Hooper were Celtic 2-0 up after 21 minutes and apparently coasting. But they were clawed back and toppled by County's character, athleticism and finishing. County were the architects of their latest excellent result.

They are too wise in Dingwall to be bothered by headlines about the "shocker" of "shameful" Celtic losing to them. County are 11 games unbeaten in the Premier League and third in the table, with healthy prospects of playing European football next season. They deserve more respect than to be patted on the head while Celtic get scathing criticism for losing to them. The club which first defeated Celtic in the 2010 Scottish Cup final at Hampden have been on an upward trajectory for years. It is no longer a shock when they beat any other Premier League team.

If chairman Roy MacGregor is the sugar daddy, Adams is the coaching architect. MacGregor and County are inextricably bound together but a day will come when Adams will be lured away to shout at the noisy supporters of his next, bigger club. Successive promotions, a Scottish Cup final appearance, the club's highest league finish, perhaps a Europa League place, too: that all amounts to an irresistible advertisement of sustained achievement. Recently the talk has been of how long Celtic can retain Lennon's services. Adams is a couple of rungs down the ladder but heading in the same direction.

"I'm pretty sure clubs are taking notice of him," said County defender Grant Munro, who scored the lovely volleyed goal which began their comeback. "It depends what his ambitions are. He's an ambitious guy but I think he is also enjoying working with the group of boys we have got here at the moment. He has said the grass isn't always greener in terms of players leaving, so you could maybe say the same about management. He is contracted to County for next season. But I'm sure there will come a time when there is an approach from a club to the chairman to test the water."

Finishing second or third will be good enough for County to enter the Europa League, and fourth would also be enough if Celtic win the double or if Hibernian or Dundee United win the Scottish Cup and also finish in the top three. Publicly, County's players and management talk only of wanting to finish in the top six – until very recently the line they peddled was about just wanting to avoid relegation – but they are fully entitled to think of Europe. On Saturday they face another compelling fixture against local rivals Inverness Caledonian Thistle.

"I look at our next few fixtures and there are no easy games at all," said Munro. "You see a club like Hearts down at the wrong end of the table, but they still have a great squad. A lot of money has been put out by the club to upgrade the stadium and get it ready for the SPL – we don't want to throw that away."

Munro's goal was the fourth he has scored against Celtic and Sam Morrow quickly followed it with an equaliser for 2-2 at half-time. Both sides fashioned chances for a winner but County could not be contained and in stoppage time a through ball caught out Fraser Forster and substitute Steffen Wohlfarth planted the ball in his net for the third time. So much for the interview with Forster in an English paper last week which claimed that after the peak of Turin last midweek he would be "twiddling his thumbs" against poor wee Ross County.

Six of the Celtic team which started in Dingwall had also done so in Italy. Given that four others were injured – Victor Wanyama, Adam Matthews, Georgios Samaras and Emilio Izaguirre – Lennon selected the strongest side available to him. His exasperated outburst about some unnamed players performing as though their minds were with other clubs, as if they had been "tapped up", invited speculation about who he meant. Forster? Anthony Stokes? Biram Kayal? Kelvin Wilson? He praised Gary Hooper, so he could be discounted.

Celtic are 15 points clear and freewheeling towards the title. But if supporters start to share Lennon's belief that players are shortchanging them in the run-in, they will turn on the team and then desert them.