The manager, who saw his side beat Crystal Palace 2-0 on Saturday, is looking to repeat Liverpool's against-the-odds march to glory in 2005.
The reigning Premier League champions have put up a limp defense of their title, and are currently 15 points behind first-place 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 its Champions League status could be to win the tournament – with its march toward 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.”
Similar to Liverpool, Chelsea finished only sixth in the Premier League but overcame the odds to win the Champions League in 2012, and Moyes knows anything can happen in soccer.
He added: “You see some of the games, where teams have hung on and hung on and somehow nicked a goal.”