Now, as they head to Slovenia today, manager Ronny Deila has a simple message for his revived players: Make sure this Champions League play-off with NK Maribor is still alive for the return leg at Celtic Park a week tonight.
Deila and everyone else at the club has heaved a huge sigh of relief that Legia Warsaw not only fielded a suspended player during their qualifying round win against them, but that Uefa have punished them accordingly, and the Court of Arbitration for Sport has not felt moved to fast-track an appeal against the decision to award a forfeit.
If Celtic were a cat, that would be three of their lives used up.
But now, having been resurrected in the most dramatic fashion, Deila is desperate to grab on to this lifeline.
While Celtic have certainly been beneficiaries of Legia's inability to play by the rules, nothing that has happened at Uefa's HQ or at CAS alters the fact they were comprehensively beaten in both legs by the Polish champions.
The events since the second leg at Murrayfield have attracted a worldwide audience, many of who sided with Legia in their argument that they should be the club marching into the play-off round for the Champions League.
To that end, the neutral support which Celtic usually attracts could be diluted as they attempt to take this opportunity to maximise their good fortune.
But Deila is confident his players can divorce themselves from all outside influences and deliver a performance tomorrow in front of the partisan crowd in the Ljudski vrt Stadium which confirms they have progressed from the side they were against Legia and are not out of their depth at this level of European competition.
The manager has also progressed in his understanding of what is required to be successful in this job.
The steep learning curve he was already on had the gradient increased immeasurably when he steered the Hoops towards the Champions League group stage.
This is manifesting itself in the results the team has recorded since losing so heavily to Legia, opening up their Premiership defence with a 3-0 victory over St Johnstone and a 6-1 thumping of Dundee United.
However, Deila accepts Maribor will present a very different, and substantially tougher, challenge, one which requires a different approach both from the way they played against Legia and in the domestic games since.
He said: "We want to make sure the tie is still alive when we come back to Celtic Park.
"So, it is important not to be naive.
"We need to play good football, but be very well organised and prepared."
A score draw would be a good result against the team which has won the Slovenian championship for the past three years.
But Deila has studied closely the way they disposed of Macabbi Tel Aviv in the last round, and how they pushed Sevilla all the way in the round of 32 in last season's Europa League.
His summation? "It would be difficult to get a draw over there, so that would be a good result.
"But, again I have to see a performance and how good Maribor are, then we will see what is a good result or not.
"But, of course, getting through is the result we want."
The P word is paramount with Deila. Most managers equate it to pressure, of which there is much, given the prize at stake.
But he never veers from his belief that performance is king and the yardstick by which his team must be measured.
So, it is with no little relief Deila's players proved at the weekend that they are getting to where he believes they need to be, albeit with one or two defensive mishaps along the way.
Deila insists the progression he demands is now accelerating because competitive games automatically step up the pace.
He added: "They are training well every day, as well. The group has been fantastic since I came here. They really want to adapt and they put effort into every training session.
"That's why we are getting the response now.
"The performance and result at the weekend was exactly what we wanted ahead of the game in Maribor."
The bonus was the goal haul, and the fact the six were shared between five players, confirming that Celtic are well-armed in several areas.
"That is pleasing to see," said Deila.
Not even the fact his main striker, Anthony Stokes, failed to get on the scoresheet populated by Stefan Johansen, Kris Commons, Charlie Mulgrew and two of his latest recruits, Jason Denayer and brace Bhoy Jo Inge Berget, concerned the manager.
"Anthony didn't get a goal, but he was good, working hard for the team," was his acknowledgment of a job well done by the clearly-frustrated Irishman.
"I really liked the co-operation between him and Kris. He was involved in many of the goals."
That should be enough to ensure Stokes is involved again tomorrow night in a line-up expected to give more than a passing nod to caution.
Deila has been bold with his selections in previous Europan ties, and some of the gambles he has been prepared to risk have backfired.
Starting 19-year-old Denayer in central defence alongside Virgil van Dijk, the Belgian loan signing having played just 90 minutes for the club - albeit franked with a well-taken goal - could be considered another punt.
But with Efe Ambrose serving the second of his two-match ban for his red card in Warsaw - you can be sure Celtic did register him for this round! - and Mikael Lustig expected to be required for the right-back position as Adam Matthews is struggling with a calf injury, Deila's hand may be forced.
Not that there is any sign of reluctance on the manager's part to go with Denayer, whose pace, reading of the game and comfort in possession mark him down as one to watch.
Asked if the teenager is ready to be pitched into such a pressurised situation, Deila didn't waver as he replied: "Yes. He is a quality player.
"But I knew that. I'm happy to have him here."
Not in any rush to show his hand, however, Deila added: "But you also have Mikael Lustig who can play in there as well. So I have good defenders to chose from.
"I want to have options. I want to have competition."
That demand is not limited to match days. It has to be an ethos running through everything the players do.
"People have to do their job every day in training and show in matches they deserve a place in the first team," said the driven manager.
"We are going to play a lot of matches, so we we can't rely on two players. We need more."