The Premier League champions must overturn a 2-0 deficit on Wednesday at Old Trafford to reach the quarterfinals of the competition, but head into the fixture on the back of a 3-0 loss at home to Liverpool.
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"I see the players every day. The qualities they show me — I think they know they can play better. I don’t think any of them are questioning that," Moyes told reporters.
"I’ve got belief in the players. I can see what they can do. I agree we’ve not showed it as often as we’d like, we’ll try and make that happen tomorrow night."
On Tuesday it was revealed that Moyes had been locked in crisis talks with his backroom team following United's defeat to Liverpool, which has left the club 12 points behind fourth-place Manchester City in the Premier League.
But the United boss insists his has "big plans" for the team and maintains he is not a short-term appointment.
"My future has not changed one bit," said Moyes. "I’ve got a great job. I know exactly the direction I want to go in. It’s not been the season we’d hoped we would have at this present time.
"But I’ve got ideas what I want to do and put in place when the time’s right.
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"The most important thing is to get the Olympiakos game played. Hopefully get through that competition. If we can it’ll be a massive lift for us. We know we’ve got ourselves in a poor position being 2-0 down and we’ve got to try and make it show and play well in the game."
"The biggest assurance is that they let me get on with the job. We make big plans for years going forward, that’s why they gave me a six-year contract. This club is not a club that works on short-term vision. It works on a long-term vision."