Moyes' critics came out in force again on Sunday when United lost 3-0 to bitter rivals Liverpool.
Those critics will be given more ammunition if Moyes' men put on a limp display on Wednesday night which is on a par with that Liverpool loss or the one which came two and a half weeks ago in Athens.
Then, United gifted Olympiacos a 2-0 advantage thanks to an inept display which saw Alejandro Dominguez and Arsenal loanee Joel Campbell find the net.
Only five teams have overcome a deficit of two goals or more in the 22-year history of the Champions League, but Moyes is not throwing in the towel just yet.
"If we can go through it would be a massive lift for us," the United boss said.
"We know we have got ourselves in a poor position being 2-0 down but we have a lot of belief and we have to make it show in the game."
Moyes was forced to answer serious questions about his future for the first time on Tuesday.
The defeat to Liverpool may have wounded pride, but there were no calls for the manager's head from the terraces on Sunday.
Moyes did concede that results will dictate whether that support remains in tact though.
Moyes defiantly brushed off suggestions that he is losing the support of the United hierarchy, indicating that he had received words of encouragement from leading figures on the club's board, including predecessor Sir Alex Ferguson.
"(Ferguson) has been incredibly supportive," Moyes said
"I speak with him regularly and I see him at the games.
"I always have a few minutes with him. He is very supportive. He told me before I came in it was a difficult job but he is always here to help.
"Him, (director) David Gill, (vice-chairman) Ed (Woodward), all the board are very supportive.
"The biggest assurance is that they let me get on with the job, we never discuss it (Moyes' position).
"We talk about the future, we are making big plans for years going forward.
"That is why they gave me a six-year contract because this is not a club that works on a short-term vision, it works on a long-term vision."
On the eve of the match, Moyes received the sympathy of the man who is plotting to inflict another blow to the Scot's credibility - Olympiacos manager Michel.
"David Moyes is suffering and I don't like to see any manager suffering. I have sympathy for him," the former Real Madrid midfielder said.
"We know he works hard, but sometimes results don't mirror the hard work done.
"It's nothing personal to David Moyes. It's a big opportunity to knock Manchester United out of the competition, but David Moyes is not an enemy."
Olympiacos may recall leading striker Javier Saviola, who has travelled to Manchester despite missing the last four games with a thigh problem.
United, meanwhile, will be without Juan Mata, who is cup-tied. Defenders Chris Smalling and Jonny Evans are out with their respective hamstring and calf problems.