The current campaign has been a fairly successful one so far for Celtic. The champions made their long-awaited return to Europe’s top table and while the Glasgow club ultimately ended up propping up the rest in Group F, players and supporters alike could take heart from the team’s performances against some of the continent’s top sides.

On the domestic front, it is hard to find fault with Postecoglou’s team. Barring a 2-0 defeat to St Mirren in Paisley in the league, they have won all of their cinch Premiership fixtures to date this term, banging in 50 goals along the way whilst only shipping 13. There is also the small matter of a League Cup semi-final against Kilmarnock to look forward to in January and with Rangers currently in disarray, Postecoglou will surely be looking to secure a clean sweep of the domestic honours on offer.

Most managers would be fairly content in such circumstances but then again, Postecoglou is not most managers. The Greek-Australian’s relentless demand for improvement means despite it all, he remains unsatisfied with his team; adamant that they can improve further still.

Given Celtic’s dominance in Scotland this term, the other 11 Premiership clubs could be forgiven for feeling a little apprehensive about the prospect of the runaway league leaders raising their game by another notch or two. But with new arrivals expected when the transfer window reopens in January – not to mention the return of captain Callum McGregor and centre-back Carl Starfelt from injury – Postecoglou is convinced that things can only get better.

“We’ll definitely be stronger,” said the Celtic manager. “I’ve said this was the difficult period for us what we’ve just been through. No doubt we’ll be stronger – we’ll need to be stronger.

“We can’t stand still, no matter if people are saying we’ve had a great start. I refuse to stand still. Whatever the watermark has been, we aim to raise it when we get back.”

“I’m always happy, and always excited,” Postecoglou continued. “There’s always something that needs to be done.

“It’s not just about bringing in new players for the sake of it. It’s one we feel can take us to the next level.

“What we have done in the league so far is a strong foundation for us and the target is now to finish the season better than we started.”

The former Australia national team manager certainly isn’t one to rest on his laurels and it is a characteristic he believes he shares with the club he leads. As Postecoglou sees it, Celtic have to be constantly evolving.

He explained: “It has to be the way. I think that’s what the club has always strived to be.

“I get the sense that sometimes you get distracted by other things, but the goal for us should always be to be stronger every year and bridge the gaps with the ones we want to compete with. You have to do that in all areas.”

The champions must work hard, sure, but they also have to out-think other teams if they are to make a dent in the European arena.

This year’s Champions League campaign served as an apt demonstration of the scale of the task facing Celtic. Finding a way to minimise the gulf in finances between European football’s haves and have-nots is no mean feat but Postecoglou believes there is a way to do so.

Recruitment, naturally, is at the forefront of Postecoglou’s plan. He has not been afraid to scour every corner in the globe in his search for players he thinks will improve the squad and the Celtic manager believes that unearthing rough diamonds in untapped markets is the key to bridging the gap with Europe’s elite sides.

“Yes, absolutely [we have to spread the net wide],” Postecoglou said of the club’s recruitment strategy.

“For us to challenge the teams we want to challenge, we need to do things a bit differently. We have to box clever.

“It’s worked well for us so far. The markets we’ve tapped into have been really beneficial for us and we’ve got great value in terms of what they’ve provided to our football club. We’ll be looking to do it again.”

With the Premiership on hiatus while a certain football festival takes place in Qatar, Celtic fans will have to wait a little longer until they can see the improvements in the team that Postecoglou is seeking to make.

Having led his nation during the 2014 edition of the tournament in Brazil, the World Cup holds a special place in Postecoglou’s heart. The backdrop to Qatar has led to calls for a boycott from some, but the Greek-Australian feels the competition still retains its magic and he will be closely watching events unfold in the Gulf.

“I’ll watch it,” he said. “It’s one of those events you get engrossed in when it comes around.

“There are always great stories and we’ve got a few participants in there. There might be a couple of others I’m looking at as well.”

If the 57-year-old required a reminder of just what international competition means to him, Australian outlet 10 Football provided a timely reminder towards the tail end of last week. They released a five-minute video containing clips of a passionate Postecoglou addressing his players throughout his tenure as Australia manager, with a full spectrum of emotions on display.

The archived footage struck a chord with Celtic supporters, who have embraced Postecoglou’s fervent and animated outbursts since he first pitched up in Glasgow’s east end a year-and-a-half ago. The man himself expects that in a few years’ time, similar clips of his time at Parkhead could be doing the rounds.

He added: “I’m sure there will be footage of me here! I’m passionate about what I do and I’m not afraid to show it if need be.

“It’s not on a weekly basis, it’s kind of selected and it’s done hopefully to make an impact. All along I’ve just tried to be who I am and that's it.”