A single victory over Ajax from their opening five Group H games leaves them facing the unpalatable prospect of finishing a Champions League campaign with the club's lowest ever tally in eight Champions League ties.
Previously, the five points collected in Martin O'Neill's final season as boss, 2004-05, and then Gordon Strachan's final term as manager, 2008-09, were the poorest returns.
O'Neill's side - which included Neil Lennon at the heart of it - opened up with three straight defeats to Barcelona, AC Milan and Shakhtar Donetsk before defeating the side from Ukraine at home then finishing with a draw in the Nou Camp and again when Milan came to Glasgow.
For Strachan's side, it was also two home draws, against Aalborg and Manchester United, but that was all they had to show for their efforts as they headed into match day six already condemned to bottom spot in their group.
A win at Parkhead against Villarreal pushed the final tally up to a more-respectable five points.
But, having qualified for the last 16 on each of the previous two seasons, it was still scant consolation, and a huge disappointment.
If Lennon's side are to avoid setting a new low record, they must win in the Nou Camp this evening.
That's a massive ask at any time. But, with Barca still needing a point to secure top spot in the group, it's going to be an even bigger challenge for Scott Brown and his team-mates.
The skipper - itching to make amends for having to serve a three-game suspension during which he sat and suffered while Celtic's good form at the start of Group H transformed into bitterly disappointing performances against Ajax and AC Milan - is ready to lead by example.
As they prepare to step out on to the Nou Camp stage in a few hours time, Brown will remind everyone in the squad their business is far from over for this European campaign.
He is adamant their position and points tally does not accurately reflect what they have brought to the Champions League table.
Brown said: "We want to finish on a high.
"We believe we have got the players who can go out there and get a point, or even a win.
"We managed to win against Barcelona at Celtic Park last year. It was a big occasion for us, and we played really well that night.
"We want to do the same this time."
To achieve this goal, Brown knows they must overcome their involuntary-but-debilitating resistance to finding the net in the Champions League.
They controlled large swathes of play in their opening game in the San Siro, and created a number of good chances, but failed to convert any and lost 2-0.
When Barcelona came to Parkhead, the Hoops played a containing game, but actually eeked out a couple of decent opportunities - ironically after Brown was dismissed.
Cesc Fabregas's goal with 15 minutes to go completed the misery for Celtic that night, and made them all the more desperate to find the net when Ajax came to Parkhead on match day three.
However, all they had to show for their huge attacking effort was a penalty from James Forrest and a deflected goal from Beram Kayal as they won 2-1.
Blanks against the Dutch champions in Amsterdam followed by yet another no-score as Milan struck three past Fraser Forster in Glasgow to seal Celtic's fate.
The response has been as heartening as it has been impressive, with 12 goals scored in the two games since the Milan defeat.
And Brown is confident that, though it's a much higher level of football tonight, this is striking form which can give them hope - and belief - that they can close their campaign on a positive note.
"In the last couple of games, we have been flying," he said.
"We have been creating chances and scoring goals, and we are going to try to take that into the Barcelona game.
"We are feeling positive, and I think we have set ourselves up as well as we could for this game."
While the 7-0 thrashing of Hearts in the Scottish Cup and the 5-0 thumping of Motherwell to extend their lead in the SPFL Premierhsip has been timely, the margin of the victories has also raised the question of how well - or poorly - plying their trade in this country prepares Celtic for facing Europe's elite.
Brown is quick to answer that one, arguing with conviction that the recent results are a reflection of how well they are playing rather than how poor the opposition facing them happens to be.
When asked if these wins are actually a handicap to being match-ready for Europe, the skipper said: "That's definitely not the way we see it.
"We know it's going to be difficult playing against Barcelona. It always is.
"We have been scoring goals, and always knew we would start doing that. It was just a matter of time before this came, and the last two games have been enjoyable to play in.
"But going to the Nou Camp, we know it will be a different story. We are not going to score five, six or seven against them."
Like everyone else in the Hoops squad which has now settled into what, in recent seasons, have become pretty familiar surroundings in the Catalan capital, Brown would be happy just to get one goal - if it was enough to give them the three points which would double this term's Champions League tally.