On the eve of what has become a death-or-glory showdown with the Danish champions, the Parkhead manager studiously avoided the implication that his opponents are a soft touch, offering a rationale that is supported by his own team's deplorable record in such outings and by Aalborg's achievement in securing a scoreless draw in Glasgow in the opening game of the campaign in September.

"Listen," said Strachan, "if people at home are thinking this is our best chance of getting our first away victory at this stage of the competition, the Danes are entitled to believe that this is their best chance of a first win in the Champions League."

Strachan is, of course, as mindful as the rest of the country that this penultimate match will be Celtic's 18th attempt at taking three points on foreign soil, the previous 17 having yielded 16 defeats and a pathetic return of one point from a possible 51. It is, as he agreed, a problem to which he has not yet found a solution, even if half of the sequence of unsuccessful expeditions were racked up during the tenure of his predecessor, Martin O'Neill.

In response to a Danish journalist's question of how the embarrassing run has come about, Strachan said: "Well, the other teams have scored more goals than us. It has nothing to do with nervousness or any other factor, it's really quite simple. We haven't scored as many goals as our opponents.

"I wish I had a brilliant answer for you but I don't. If I did, I may have been able to implement it by now. What we do know is that these matches can be won with a simple, single piece of brilliance. If you look at our match against Villarreal in Spain earlier, you realise that if Sammy (Georgios Samaras) takes his chance and gives us the lead, it could have a huge impact.

"Then you remember that Marcos Senna did take his opportunity when he got a free kick in a dangerous area and that was the single most important difference between the teams. We have players who can produce brilliant moments, but we also have a few who are not a hundred per cent fit and we'll have to see how they come out of tonight's training session."

Strachan's injury problems were underlined by his selection for the 3-1 victory over St Mirren on Saturday, when Gary Caldwell was moved from central defence into midfield to compensate for the absence of Paul Hartley, Aiden McGeady and Barry Robson from the starting line-up, the last-named came off the bench for the last 30 minutes. All three, as well as Shunsuke Nakamura, are contributing to the manager's delay in finalising a team.

"Aiden hasn't played for over three weeks," he said, "and we hope he proves himself fit again in training. I'm not saying that would make him odds-on to start – in fact, he probably isn't – but it would be good to have him fit again. We do miss his change of pace and what he can do on the ball. Being out for three weeks, you don't lose any of your base fitness, but you can lose a bit of sharpness, so there's a decision to be made about him.

"The others aren't at a peak, but they all want to play. You couldn't keep Paul Hartley out with a big stick, Naka just surprises you all the time, arriving for training when you think he's going to be out for a while. And Barry showed on Saturday he has the same attitude, stepping up when we needed him. All these things, like the good run of victories we've been having in the domestic game, make you feel better about yourself, but whether it can have an impact in the Champions League is another matter.

"The fact is that all the teams in the tournament are mentally strong, because they have come through so much to get here that it is inevitable. There will be varying degrees of skill and style, but the one constant is that they are all mentally strong. That applies to Aalborg as much as anyone else."

Strachan conceded that the Danes would be "different" types of opponents to Villarreal and Manchester United, while taking great care to stress that did not mean he considered them easier to beat. But there seems little doubt that he will try to be less guarded in his deployment, recognising the need for the score draw that would guarantee Celtic at least third place in the group and a parachute into the Uefa Cup.

Recognising that only victory here in Aalborg, defeat for Villarreal by Manchester United and another win by two goals against the Spaniards in Glasgow on 10 December would keep his team in the premier tournament, Strachan took the view that a place in the last 16 for the third successive year was the least likely of the three possible outcomes.

"I think it very unlikely we will go through," he said. "Apart from what we have to do for ourselves, the other match (at Villarreal) is out of our hands. No, we simply have to look after ourselves and see where it takes us. But I think we can stay in Europe and, as we saw with Celtic in 2003 and Rangers last season, the Uefa Cup also offers opportunities you wouldn't turn down."

• Tonight's match will be refereed by Konrad Plautz of Austria. Plautz took charge of the AC Milan v Celtic match in the last 16 of the Champions League in March 2007, and was criticised by supporters for twice dismissing the visitors' claims for a penalty. Celtic eventually lost out to a goal from Brazilian playmaker Kaka.

Plautz was also in charge when Scotland shocked France 1-0 in Paris in the Euro 2008 qualifiers. He will be assisted tonight by countrymen Armin Eder and Raimund Buch.