Not every path that leads to football fame follows the same route. Jock Stein was working down the pits by the time he was James McCarthy’s age and it took the Celtic legend eight years before he earned a full-time wage from the game.

Stein went to school barely a mile away from Hamilton Academical’s ground. Hard economic facts of life forced him to leave at 15 to get a job, while at the same age McCarthy became the youngest player in Hamilton’s history to pull on a first-team shirt and could earn a lucrative move to England in the near future.

Now 17, McCarthy did not look out of place at Celtic Park on Saturday but even his youthful vigour was no match for a side that has so many midfield players crying out for a game, that one was even prepared to play at left-back just to get on the pitch. Few international players would consider ruining their reputation by playing out of position in the run-up to a World Cup week. Barry Robson was not perturbed by that prospect.

The Scotland player has taken the long way round in his career, rebuilding it after being released by Rangers as a teenager, and is no mood to waste any chance to play as he nears his 30th birthday. He is the sort of influence that Stein would have approved of – and Gordon Strachan certainly does.

The Celtic manager made up his mind after last Tuesday’s Champions League defeat by Villarreal that he wanted Robson’s enthusiasm in the side to face Hamilton. Even though Robson was given just a cameo performance as a substitute in Spain, Strachan is convinced that he brings a winning mentality to the table that is hard to ignore. So, Robson was pressganged as a left-back to fill the void left by the injured Lee Naylor.

Of the quartet whom Strachan actually asked to play in a genuine midfield role, Shunsuke Nakamura and Aiden McGeady both found the net with stylish finishes, while Marc Crosas was possibly Celtic’s best performer in a display crammed with crisp, fluent football – all augmented by a raiding left-back. Young McCarthy could do worse than study the champions’ midfield.

“Hamilton have done well this season and have a lot of good young players, but I thought we were outstanding,” Robson said. “You have to give credit to them. This is the first time they have come here and played in front of this size of crowd. I don’t think people gave us credit for the way we played against Villarreal. They are a really good team.”

The shirt colour may have been exactly the same but Hamilton did not present the same barrier to Celtic that Villarreal had. Nakamura’s sublime 25th-minute volley was followed by Georgios Samaras’s tenth goal of the campaign, before Scott McDonald displayed a tenacity that delivered the third goal in 76 minutes. The best was saved for last, when Shaun Maloney came off the bench and bemused Simon Mensing and Martin Canning with a sequence of stepovers before unselfishly setting up McGeady.

“The attitude could have been a problem,” Strachan said. “It was windy, wet, we had just played a European tie and had been on the plane for a long time. To start the way we did with energy, that pleased me. We knew we had to get our attitude right so we thought, ‘Where do we get Barry in?’ Unfortunately for Lee, he got injured on Friday so he made it easy for me. I thought Barry was tremendous. He can play in any position and has an energy and a will to win.”

Robson, though, has complete faith in his own status. “I’m quite confident of getting a game in midfield in my own right but I am happy to play where ever the manager asks me to,” he said.

Hamilton might have marked their first visit to Celtic Park in 20 years with a goal had James McArthur not seen his 79th-minute penalty saved by Artur Boruc, before the Celtic goalkeeper then pawed away McArthur’s follow-up header. Perhaps that was justice, given that Gary Caldwell appeared to win the ball rather than foul McCarthy when the award was given.

“I think it summed up James McArthur’s day,” Billy Reid, the Hamilton manager, said. “He was young player of the month in the first month of the season but that was probably the worst game he has played for me. That happens in football and he has to pick himself up. He has a good future ahead of him. If I’m being honest it could have been more than 4-0. I don’t think we did ourselves justice. It was a huge learning curve for us.”

Alex Neil, the venerable 27-year-old who plays the holding role in Hamilton’s midfield that allows McArthur and McCarthy to get forward, endorsed Reid’s view. “There were too many boys under par,” he said. “We didn’t keep the ball as well as we have done in previous games and we paid the price.

“That’s the first time I’ve played against Celtic and they have been the best side in Scotland for three years. They have quality throughout their side. This has shown, not just the young boys, but the team in general, how far away we are. We’re going to have to buck up our ideas. Everybody has been taking the plaudits but now it’s time to knuckle down and show why you’ve been getting them.”

Celtic (4-4-2): A Boruc 8 M Wilson 8 S McManus 7 G Caldwell 7 B Robson 8 S Nakamura 8 S Brown 7 M Crosas 9 A McGeady 8 J Vennegoor 7 S McDonald 8Substitutes G Samaras 7 (for Vennegoor, 2min), S Maloney (for Samaras, 72), D O’Dea (for Brown, 82). Not used M Brown, M Donati, P Hartley, P Caddis.

Hamilton (4-4-1-1): T Cerny 7 D Elebert 5 C Swailes 6 M Canning 6 B Easton 5 S Mensing 5 A Neil 8 J McArhur 5 D Graham 6 J McCarthy 8 D Lyle 4Substitutes M Corcoran 5 (for Swailes, 46min), S Ettien 4 (for Lyle, 46), J Thomas (for Graham, 77). Not used S Murdoch, C Casement, T McLenahan, L Atkins.