As the Hoops were held at home by the Danish side and have failed to win any of their three most recent friendlies, the pressure is already starting to mount following a woeful 2020-21 campaign.
Entering the qualification process at the second round stage last Tuesday, Celtic saw former Australia coach Ange Postecoglou's tenure begin with a draw against Midtjylland that saw both sides reduced to 10 men - and the home side's dominance of possession going unrewarded despite Liel Abada's debut strike.
Their hopes of building a lead to take to Jutland were diminished when Nir Bitton impetuously picked up a second yellow card in short succession; clashing with the visitors' Anders Dreyer. The Danish winger was also sent off later on, but Evander then managed to beat Celtic goalkeeper Vasilis Barkas with a free-kick to level the game.
With 9,000 fans welcomed back to Parkhead to witness their first competitive fixture in well over a year, it proved a frustrating conclusion for Postecoglou and his new charges, who were crushed 6-2 by West Ham United in a pre-season warm-up at the weekend.
Such a setback - while irrelevant in terms of points or prizes - can have done nothing for the Glasgow giants' confidence, as they seek a return to the Champions League group stages for the first time since 2017.
Having fallen at the equivalent hurdle to Ferencvaros last year, Celtic's continental woes have been compounded by seeing domestic dominance stripped away by their loathed arch-rivals in recent months.
Certainly, they have endured a difficult year, and their new boss will need to adjust to his new role rapidly if Midtjylland are to be overcome on home soil - just three days before the Bhoys begin their Premiership season away to Hearts.
Signs that his team will build from the back and play at the high tempo so beloved by Celtic's fans may offer some encouragement, however their capacity for individual errors appears to remain undimmed.
With the opportunity to meet either PSV or Galatasaray - most probably the former, given their 5-1 first-leg lead - in the next round providing motivation if any more were needed, Midtjylland will expect to make the most of escaping Glasgow with a draw last week.
After kicking off the 2021-22 season with an unexpected league defeat to Odense, the Ulvene have resumed normal service during the past few days, having followed their hard-earned result at Celtic Park with a 1-0 win over Aab Aalborg on Saturday.
It was perhaps a more comprehensive display than the scoreline suggests, as last term's Superliga runners-up switched to a three-man defence - ahead of former Huddersfield Town goalkeeper Jonas Lossl - which allowed the opposition next to nothing offensively, while the forward line created several presentable chances.
The prospect of things clicking into place will give new manager Bo Henriksen a boost before the biggest night of his career so far, as he seeks to lead his troops past Celtic and into the third qualifying round - with a guaranteed Europa League spot available should they go on to lose at that stage.
Having managed to dig out draws against Liverpool and Atalanta in last year's Champions League group phase though, the ambitious club have their sights set higher once again.
Celtic coach Ange Postecoglou will be without defensive lynchpin Nir Bitton in Denmark, due to the Israeli's red mist earning him a red card in last week's first leg, so Stephen Welsh is expected to lead the back line in his absence - with young Dane Murray his potential partner.
At fault for Midtjylland's goal at Parkhead, under-fire goalkeeper Vasilis Barkas was replaced by Scott Bain at half-time during the humbling loss to West Ham - with the former Dundee stopper faring little better - so it remains to be seen who will be handed the gloves on Wednesday.
Soon after Bain's appearance, Postecoglou made wholesale changes by swapping his entire outfield selection, but Liel Abada, Odsonne Edouard and Ryan Christie at least impressed in the hour they played and each is likely to start again in a 4-3-3 formation.
Kristoffer Ajer left the club last week - completing a move to Midtjylland's partner club Brentford - while both Mikey Johnston and Karamoko Dembele have been out injured and are not expected to feature.
The home side, meanwhile, have fewer concerns ahead of the game, but teenage winger Aral Simsir has been absent due to self-isolating with COVID-19 and Anders Dreyer will serve a suspension after his second-half dismissal in Glasgow.
Australia international Awer Mabil - who made a mark in European competition last year following his return to the Superliga club - is set to replace the latter on Wednesday, lining up on the opposite flank to Pione Sisto in support of Junior Brumado.
However, Bo Henriksen could throw a spanner in the works should he opt to retain the three-man rearguard he picked in the league at the weekend. In that case, former Brentford defender Henrik Dalsgaard would shift across from right-back, with Joel Andersson featuring in a more advanced role.
FC Midtjylland possible starting lineup:
Lossl; Dalsgaard, Sviatchenko, Andersson; Juninho, Charles, Evander, Paulinho, Mabil; Brumado, Sisto
Celtic possible starting lineup:
Bain; Ralston, Murray, Welsh, Taylor; McGregor, Soro, Turnbull; Abada, Edouard, Christie
We say: FC Midtjylland 2-1 Celtic
Midtjylland may not have the advantage of an away goal, given that rule's recent disposal, but are a more settled side than Celtic and that greater cohesion is likely to prosper in front of their fans on Wednesday.
It could take a while for Ange Postecoglou to re-shape the Bhoys in his own image, but time is short in the unforgiving realms of continental combat and their hoped-for comeback season could get off to a slow start.
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