Fear not, however. Their intoxicating brand of Champions League football will be available to admire at Scottish football grounds.
Ange Postecoglou has pledged to ensure that the high tempo, high pressing style of play that has ensured they are exiting the competition with a degree of self-respect will be maintained on the home front.
The Celtic manager believes domestic opponents are now reaping the whirlwind. Opponents such as Hibs, Motherwell and, most recently, Hearts have suffered the cost of the hard lessons Celtic are learning during an exacting return to this level after an absence of five years.
There’s still the chance the Parkhead side can secure Europa League involvement after Christmas if they take at least four points from their final two games, the last of which is a trip to the Bernabeu to face Real Madrid.
That is another matter entirely. But Scottish assignments, even those at such tough venues at Tynecastle, are proving easier to negotiate because they are bringing Champions League football back home to Scotland.
Postecoglou noted how his players had reacted after Georgios Giakoumakis's header levelled the scores at 2-2 in Saturday's 4-3 win over Hearts.
“You just had to look at our body language on the weekend,” he said. “We equalised after being 2-1 down at Hearts, away from home, with all sorts of drama round the game. But when Giakoumakis scores, we don’t even celebrate. We ran back to the centre line to get the ball and kick off again.
“I think there is something in that, he added. "There is real merit in that. There is a team who were away from home, under siege in terms of the crowd and VAR and all that sort of stuff. We had just equalised. Let’s get back to the centre circle and go again. I take great pride in that because that goes beyond the football. That goes to the character of the group we’ve got.”
It certainly proved the point he made to his players after the final whistle following the 2-0 home defeat against RB Leipzig two weeks ago. “I said to the players if we maintained our levels (shown) against Leipzig, in terms of physically and tempo, in the league, we will destroy teams,” Postecoglou revealed.
That has since come to pass – even if Hearts might baulk at the suggestion that they were ‘destroyed’ at the weekend. But Celtic have certainly exhibited few ill-effects from the deeply disappointing home reversal against RB Leipzig, which meant their Champions League hopes were extinguished as early as matchday four.
Two late goals deflated the home crowd but Postecoglou hoped there was no despondency. "That's a strong word," he said yesterday.
The players have since roused themselves and delivered the perfect response by hitting 14 goals in three subsequent outings. Hibs were hit for six nine days ago and Motherwell were beaten 4-0 at home in the Premier Sports Cup. Hearts, too, were overcome in that VAR-influenced classic.
“We could have come out of that Leipzig game and said we didn’t win, things aren’t great,” said Postecoglou. “But what it showed them is that if they play at this tempo in the local competition, in the championship, then we will blow teams away.”
Postecoglou believes Celtic have made an impact at Champions League level. He is convinced those in other countries, at other clubs, are sitting up and taking notice of the team’s style, even if it hasn’t always been successful in terms of results. Has anyone contacted him personally to compliment his team? Postecoglou stopped short of providing first-hand examples.
“You only get it anecdotally,” he said. “But I think people notice how we play, absolutely. Anyone who follows world football, European football, would be curious about the approach, without a shadow of a doubt. I think not many take the same approach.”
Postecoglou’s point ended up being illustrated little more than two hours later in the same No 7 suite at Celtic Park where he had spoken so engagingly with reporters.
Igor Jovicevic, the Shakhtar Donetsk manager, sat down and almost immediately praised Celtic's “high energy”. More than that, he said he had spoken to Real Madrid players "who had said the same". He had been impressed by Celtic's opening 45 minutes against the Spanish champions, when, he said, they might have been "3-0 up".
They might be on a worst-ever run of home defeats in the Champions League, but there’s certainly evidence Celtic are doing something right. Postecoglou will forever remain in search of what he dubbed “the sweet spot” – when style of play can be married to on-field success at such a high level.
He has resolved to keep on playing the same way. True failure would be backtracking and retreating into a shell. It would be ripping up their manifesto.
“If we qualify next year, and that’s our first job, it won’t be a success if we tear it all up and take a different approach (just) because we feel that this way isn’t going to work," he said.
“Somebody mentioned Brugge to me the other day, and just have a look at Brugge’s record in the Champions League, and how long it has taken them to get to that sweet spot.
“But if you are constantly there, and you are constantly knocking on the door, and you are taking a consistent approach, I really believe that for a club like ours there will come a year where it all comes together.
“Instead of hitting the post, the ball is going to go in. We’re going to score in the first minute and get the crowd behind us instead of missing those opportunities. It will all come together.
“But that will never happen, that sweet spot will never happen, if you get to where we are now, tear it all up and say it didn’t work because we didn’t win a game.”