United have endured a poor campaign to date by their own lofty standards and sit sixth in the Premier League, 15 points behind leaders Chelsea.
However, ahead of next week's last 16 first leg tie against Olympiacos in the Champions League, Moyes has highlighted Liverpool's European success nine years ago as an example of what can be achieved by teams not topping their domestic table.
The Anfield club finished fifth in England's top flight that season and, in what could be interpreted as a thinly-veiled dig at United's rivals, Moyes told reporters: "It isn’t always the best teams that get to the final in Europe.
"Liverpool in 2005 gives us hope, but in any cup competition you always have a chance.
Elaborating on United's chances of claiming Champions League glory, the Scot added: "I knew it was going to be a hard competition before it started. Bayern Munich, Barcelona, Real Madrid and PSG are all top clubs.
"(But) you see some of the games, where teams have hung on and hung on and somehow nicked a goal."
United face Olympiacos in Greece on Tuesday before the return leg at Old Trafford takes place on March 19.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.