It is now 10 years since Scottish football thought it was on the verge of a great leap forward. The national team’s 1-0 success against France was still being celebrated by the time Rangers swaggered to a 3-0 win in Lyon. Closer inspection was as worthy then as it is now; on both occasions, notwithstanding the tactical nous of Alex McLeish and Walter Smith, victory was achieved against teams who dominated the ball.

There was a significance to Celtic’s 3-0 win at Anderlecht on Wednesday evening that moved beyond the reinvigoration of a Champions League campaign. Celtic, while actually well short of their best, dictated proceedings against the Belgian champions. In recent European and international history, Scottish teams have not been accustomed to such displays when away from home. In the aftermath, Brendan Rodgers was happy to highlight the value of only a second Celtic away Champions League win in 28 games.

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“The message I gave to the players when we came in here 15 months ago was: ‘Lots of people will tell you what you can’t do,’” Celtic’s manager explained. “We set about trying to focus and concentrate on breaking as many records as we could and creating our own history. Of course, it is very, very difficult but let’s create our own history. This is an incredible club that has a great past but we have to really concentrate on the future and not worry so much about that.

“I think over the past 12 months you can see the improvement. It is a huge jump in level into the Champions League but I think it is pretty clear to see how the players are developing and improving. To come away and get a 3-0 victory, play that well after such a big game at the weekend [against Rangers] really shows how the players have grown and are believing at this level.”

Those on the outside may have similar sentiment. Celtic’s domestic run – they are 57 matches unbeaten – is rather taken for granted to the extent that the opposition is widely disregarded. Success on the bigger stage will lift acknowledgement of Celtic’s talent and, naturally, that of Rodgers.

“Fifty-seven games domestically is very tough to do, considering the number of games you play where the opponent will always pick up the game 10-15%,” Rodgers added. “The players have had to stand up to that whilst playing at a really high level consistently. But of course, you come into the Champions League; I think people recognise this is a good side that is developing well but you come away to a club with a great history like Anderlecht, who got to the quarter-finals of the Europa League last year, and to come and play to that level, to be as convincing as that, I think of course people recognise that as: ‘Actually, they are a very good team.’”

Rodgers thus far refuses to contemplate or discuss back-to-back meetings with Bayern Munich, which should determine whether Celtic are Europa League participants after Christmas or have designs on the Champions League last 16. Beyond, that is, a general warning: “We will get better as the group goes on.” What can be said with confidence is that the manner of the win in Belgium has instilled fresh belief into a squad which remains relatively inexperienced in Champions League terms.

“We won, not with relative ease but with a real good professionalism, with players who look like they belong at the level,” said Rodgers. “And more importantly, with an actual game model that allows you to think you can at least play well at this level. Players comfortable on the ball, players making angles, offensively looking a threat and tactically they were outstanding; blocking lines of pass, really pressing the game. That all starts from the pressure up front from Leigh Griffiths, who was outstanding.

“That gives me pleasure, that gives me confidence. There have been a lot of milestones along the journey but each one you tick off is great. To get our first Champions League win away, to keep a clean sheet, the first in so many years, is really pleasing.”

Rodgers altered an earlier plan to introduce Stuart Armstrong in Brussels, with the midfield substitute incurring a calf problem. Armstrong is, though, expected to be fit for the meeting with Hibernian on Saturday. Deeper concern – including for Scotland – surrounds the fitness of Scott Brown: the Celtic captain is to undergo scans on a hamstring injury.