Moyes, who held a crisis meeting with his backroom staff on Monday, knows that defeat to the Greek champions would cast further doubt over his future at Old Trafford with United's disastrous season having taken a further turn for the worse in Sunday's defeat to Liverpool.
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Moyes told the club's official website: "The players are capable of turning it around. We're all desperate to put things right and make sure we play better to give the supporters here something to shout about.
"They shouted [against Liverpool] and we didn't give them anything on the field. When we went to Greece, the Olympiakos fans played their part so hopefully our fans will roar us on.
"We have to go for the throat to get the win. We won't be gung-ho but we will certainly go with a mindset to overhaul the deficit as quickly as we can.
"We won't be reckless as we could find ourselves with a bigger mountain to climb but we can be forceful. We have to be if we're to keep ourselves in the Champions League."