Manager Moyes was not even born when the Red Devils last lost three successive games at Old Trafford, in the autumn of 1962, and if it happens again, United will lose top spot in Group A and be pitched into a nasty knock-out round clash with one of Europe's heavyweights.
Given they are currently occupying ninth spot in the Premier League table, the situation is barely comprehensible at a club so used to success, boasting a squad that, with the exception of Paul Scholes' retirement, is the same one that lifted the championship by an impressive 11 points last season.
Various theories have been put forward for the sharp downturn in fortunes and Moyes himself has identified a number of key areas where improvement is required.
But to the Scot's credit, he is refusing to hide behind excuses.
"I take complete responsibility for the results," he said. "It is tough because the expectancy is to win all the games and the results have not been good in the Premier League.
"There is a bit of everything we could do with doing better.
"Generally we'd like to play better. We would like to pass it better, to create more chances, I'd like to defend better when those moments arise.
"I don't think it is any one thing, it is all round we are trying to improve."
As Moyes pointed out, it is only a month since United defeated Arsenal, and a fortnight after the five-goal hammering of Bayer Leverkusen that will go down as one of the club's great European away performances.
What has alarmed supporters almost as much as those home defeats by Everton and Newcastle is the manner of the losses.
At the weekend in particular, once Yohan Cabaye scored, the lack of a response was strange for a club so used to dragging out late victories.
"I agree," said Moyes, when asked whether his team needed to show more belief and conviction.
"In recent games we haven't quite finished the games the way we would have liked to.
"We have tried to make changes to improve things but it hasn't quite happened."
Shakhtar midfielder Fernando is aware of United's current struggles but insists a trip to Old Trafford still represents a daunting assignment for the Ukrainians.
He told the club's official website: "Myself and the other players have been reviewing all the matches of our future opponents.
"But Manchester United are a very strong team. We must be 100 per cent concentrated."
Shakhtar come into the game having recently signed off for their domestic winter break on the back of a 1-0 win at Chornomorets, a result which sees them go into Christmas with a five-point lead at the top of the table.
"We are in a good place," added Fernando.
"We trained this week as normal and I think we are ready to go on the field and show some good results.
"We have to start like we normally do at the Donbass Arena. The most important thing is to attack from the start. If we do that we will achieve a victory."