But, as they put their first points on the board with a 3-0 win over St Johnstone at Perth – courtesy of second-half goals from Anthony Stokes, Nir Biton from the spot and Callum McGregor – their minds, and those of their fans, were elsewhere.
While this win was welcomed, following the shock to the system which the performances against Legia Warsaw had delivered, the result they really wanted came today when Uefa announced they had thrown out the Polish club’s desperate appeal against the justice meted out to them for fielding a suspended player.
It was, therefore, to their credit that the players selected by Ronny Deila found enough focus to get their league season up and running with a performance which was a vast improvement on what they delivered against Legia in Warsaw and at Murrayfield.
Given how poor they’d played in those Champions League qualifiers, that wasn’t hard. But, with a homecoming and a flag unfurling scheduled for Saturday, when Deila will finally take his long-awaited bow at Celtic Park, it was important progress was seen to be occurring.
It was also the first game post-Fraser Forster, his £10million sale to Southampton prompting increased calls for the club to re-invest,
so a clean sheet was a bonus.
Deila has brought in some players, but not spent any of the “lots of money” he admits he has at his disposal.
Three of his recruits – free agent Craig Gordon and the loanees Jo Inge Berget and Jason Denayer – were involved for this one, the former Scotland keeper starting and the outfield duo on the bench.
They were seated alongside Efe Ambrose who, despite the absence of the suspended Charlie Mulgrew, was not automatically reinstated to the starting XI following his European ban.
It was further confirmation that, while this is a side in transition, what has gone before is of less importance to Deila than what is happening now.
For the Norwegian, form carries more currency than reputation. There was a timely reminder that, while qualification for the Champions League is the immediate priority for Celtic, nearer to home there are plenty of challenges waiting to snare the unwary.
Saints proudly paraded the Scottish Cup they won at Celtic Park on the final day of a season which saw the Hoops collect only one piece of silverware.
With a clean sweep Deila’s target this time around, a statement of intent was required.
And, with James Forrest – whose sub appearance against Legia last week was his only action since March – back to provide much of the tempo the manager’s preferred system requires until he ran out of steam on the hour mark, the clouds which have hung over the club for the past couple of weeks are starting to part.
Okay, there remains the threat of a cold shower to remind everyone that a lot of work remains to be done.
But Celtic had enough control of this game against a side who have a habit of causing them problems to suggest Deila’s message is getting through.
The representative from NK Maribor taking notes in the main stand will have plenty – good and bad – to relay to his bosses in Slovenia.
He will be confident his side will be able to pose Celtic more problems than Saints did.
The absence of any genuine point to the home team’s attack – with the free-scoring Stevie May now at Sheffield Wednesday – will be a concern for boss Tommy Wright.
But Deila is only concerned by what his players serve up. And, on this occasion, it was more than good enough.
Their own potency in front of goal was not sufficient to convert their possession into the lead they deserved until Stokes struck on 55 minutes.
Kris Commons deserves huge credit for his part in the goal, robbing Steven Anderson of the ball as the defender dallied 25 yards from goal with a slide tackle which saw the ball run straight to the alert Stokes.
He rounded the keeper before slotting home from a tight angle with Commons following up, just to make sure.
That was no more than Celtic deserved, given their superiority, but prior to this they had been profligate.
A Stokes free-kick which whistled just past the post, a Forrest effort which was pulled wide following a clever 1-2 with Commons and a McGregor shot which was gobbled up by Alan Mannus were the best efforts they could muster to that point.
At the other end, Gordon – making his first competitive start since February 2011 – was allowed to ease himself back into action.
Indeed, in the opening half, there was more danger posed to the 31-year-old’s health than to his goal.
Steven MacLean’s tendency to panic when a semblance of a chance came his way was topped when, after the ref had whistled to signify a free-kick had been taken too quickly, the striker carried on and rattled a point-blank shot into Gordon’s guts.
Saints roused themselves to at least grab the keeper’s attention after the break but could not deny Gordon his clean sheet.
The home side did have a strong case for a penalty when Dave Mackay went down under a challenge from Virgil van Dijk, but ref John Beaton waved away their claims.
The Saints captain was even more aggrieved when, with 15 minutes left, the same official decided he was guilty of knocking over Celtic sub Derk Boerrigter after he had delayed his shot when put through by Emilio Izaguirre.
Mackay was sent off, and keeper Mannus was sent the wrong way by Biton, who rolled his penalty home.
The keeper looked even more sheepish six minutes from time when he allowed McGregor’s low shot to squirm through him and creep over the line.