The Scot, who saw his side beat Crystal Palace 2-0 on Saturday evening, is looking to repeat Liverpool's against-the-odds march towards glory in Istanbul in 2005
The reigning Premier League holders have put up a limp defence of their title, and are currently 15 points adrift of leaders Chelsea and scrapping just to finish in the top four.
With their chances of qualifying for Europe's premier club competition dwindling, United's best hope of retaining their Champions League status could be to win the tournament – with their march towards the final getting back underway against Olympiakos on Tuesday.
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“It isn’t always the best teams that get to the final in Europe,” the United manager told reporters. “Liverpool in 2005 gives us hope, but in any cup competition you always have a chance.
“I knew it was going to be a hard competition before it started. Bayern Munich, Barcelona, Real Madrid and PSG are all top clubs.”
Similarly to Liverpool, Chelsea, then managed by Roberto Di Matteo, finished only 6th in the Premier League but overcame the odds to win the Champions League in 2012, and Moyes knows anything can happen in football.
He added: “You see some of the games, where teams have hung on and hung on and somehow nicked a goal.”