But concern for his job will not be one of them.
All nails for the hanging of managerial jaikets come from the box marked "shoogly" but Deila has cause to believe his employment at Celtic will not be prematurely truncated.
First, he has the unreserved backing of the Celtic board. Second, this faith would only be tested by any sustained under-achievement in the league. Paul Le Guen, the Frenchman who was heralded to lead a revolution at Rangers, was out of the door after half a season but the Ibrox side were besieged by Celtic in the league.
This burden of a strong domestic rival, at least, cannot befall the Norwegian. Deila, then, has time. He needs it.
He can be blamed for errors in the Champions League qualifying campaign. He was wrong to pursue an attacking policy when 2-1 and a man down against Legia in Warsaw.
His strategy against Maribor at Celtic Park was also flawed. It was obvious that the Slovenian champions were a counter attacking side and the deployment of Kris Commons in the second half was understandable in the search for the Celtic goal that would have killed the tie but it also deprived the Scottish champions of a defensive presence. There was a case for bringing on Commons but Anthony Stokes, who was enduring an awful night, should have been brought off to accommodate him.
The deployment of Efe Ambrose at full-back was so calamitous it would have induced a panic attack in a bomb disposal officer. Yes, the defender plays there for Nigeria but those who champion him in that position at club level received their answer on Tuesday night.
The 25-year-old was glaringly, extraordinarily bad. This was spotted immediately by the Slovenian side. Deila should have quickly reshuffled the team or withdrawn the Nigerian.
The gameplan too seemed confused. Celtic played the second 45 minutes in a state of anxiety. Collectively, they seemed to believe that they needed a goal to progress. This was understandable given their obvious defensive frailty but it must be pointed out the best way to negate a counter-attacking team is not necessarily to throw men forward. Deila, too, could be faulted on both starting line-up and substitutions.
For example, if the full-backs are to cause trouble with their pace and positioning then Adam Matthews seems a better bet than Ambrose. His stance on Jason Denayer was also questionable. The 19-year-old was judged to be ready for a Champions League away qualifier but not a home game. The defender, on loan from Manchester City, made mistakes in Slovenia but when the options are considered he was a decent bet to start at Celtic Park.
This, though, is now the past. Deila, reassured by support from within Celtic, must plan a future. It must be remembered that he has yet to make a permanent signing for Celtic. Craig Gordon was enlisted under his watch but it is reasonable to assume that the decision on the goalkeeper's employment preceded the arrival of the Norwegian, particularly as Fraser Forster was being pursued in the transfer market by Southampton.
Deila, who initially expressed his doubts over bringing in loan players, has now hired a clutch of them, Wakaso Mubarak, the 24-year-old Ghanaian, being the latest.
Like all managers, he has inherited players he either does not fancy or do not fit into his strategy. Or both. The most obvious deficit is the lack of a striker to hold the ball up and bring midfielders into play. There was some commotion over Celtic not signing Stevie May but surely Nadir Ciftci of Dundee United would be a much better option.
Deila believes he needs physical strength in this position and Stokes, Teemu Pukki and Leigh Griffiths do not supply it. Commons, too, seems to be a player that does not convince Deila. The manager talks constantly of closing down relentlessly of being super-fit, pacy. These attributes do not immediately paint a mental picture of Commons. He also needs cover in goal for Craig Gordon, a conspicuous success on Tuesday, with Lukasz Zaluska not having taken his chance to impress against Inverness Caledonian Thistle.
Defensively, Emilio Izaguirre is suspect, Ambrose highly flawed. In midfield there is either mediocrity or potential that has not yet been realised.
Yet with a full side, untouched by injury and with the addition of a striker, Deila has the makings of a decent team. How about this in 4-3-3?
Gordon; Lustig, Denayer, Van Dijk, Matthews; Brown, Johansen, Mulgrew; Forrest, Unnamed Striker, Tonev. This leaves such as Callum McGregor, Liam Henderson, Nir Biton, Wakaso and others to fight for a starting place.
Deila then has to make decisions, and not just in recruitment. Do such as Commons, Griffiths and Stokes have to go? What about such as Derk Boerritger, Tom Rogic and Dylan McGeouch? The strong suspicion is that all could be disposed of without causing the manager too much grief.
This leaves Deila to rebuild in a transfer window that has days to go and a similar opening in January. He also has to hold on to such as Van Dijk. It is a balancing act that requires guts, faith and adherence to a plan. Celtic have to be ready for the Champions League campaign next July. And so has Deila. He must have formed a side that both adheres to his principles and delivers victories.
First, though, he has to travel to Dens Park on the back of two defeats that have not produced a goal for the champions. Dundee and Paul Hartley will not be trembling at the prospect.