He also said United were focused on planning for the long-term and not worrying about the period of transition they are in following the retirement of Alex Ferguson after 26 years in charge.
The struggling Premier League champions must overturn a 2-0 deficit from the first leg of their round of 16 game in Greece to keep alive their last remaining hope of lifting a trophy this season.
The demoralising 3-0 home Premier League defeat by Liverpool on Sunday increased the pressure on Moyes who has endured a troubled start to his United reign after replacing Ferguson last year.
"My future has not changed one bit," Moyes told a news conference on Tuesday.
"I have got a great job and know exactly the direction I want to go in.
"It has not been the season we wanted but I have ideas I want to put in place and the most important thing is Olympiakos.
"If we can go through it would be a massive lift. We know we have got ourselves in a poor position being 2-0 down.
"The biggest assurance is the club will let me get on with the job. I have a six-year contract. This club does not work on a short-term vision, it works on a long-term vision.
"The support inside Old Trafford has been phenomenal. Sir Alex has been incredibly supportive, so has (director) David Gill and the board.
"Sir Alex told me it was going to be a very difficult job but he is always there to help."
United go into the match following a poor performance against Liverpool and could easily have lost to their bitter rivals by a bigger margin.
They have to win by at least three goals against the Greek champions to go through without penalties, but have only twice overturned a two-goal deficit in European competition.
The last time that happened was almost 30 years ago when they came from two goals down to beat a Barcelona side including Diego Maradona 3-0 in the European Cup Winners Cup quarter-finals.
Moyes accepted the players need to give something back to the suffering fans.
"The first thing I mentioned to the players is we need to start giving something back. We need to work together to make it a night to be remembered. We will leave nothing behind."
United defender Patrice Evra said that he would take inspiration from the recent World Cup playoffs when his France side overturned a first leg 2-0 loss to Ukraine to win the second leg 3-0 and qualify for the finals in Brazil.
"We let the storm pass," Evra said. "It was a difficult day after the game, we didn't expect to lose 2-0 in Ukraine but after two days everyone was focused. We stood together, we played for the people who love us, our families, the fans and we give everything. Like the manager says, it is really important we score early.
"When you come to Old Trafford and you concede an early goal, it is difficult."
Moyes attempted to put matters into perspective.
"I think Manchester United is the biggest club in the world, it might not feel like that today, but this club has had great success in the past and will do again in the future," he said. "It will rise again."
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- Alex Ferguson