The former Everton boss says likes of Bayern Munich, Barcelona and Real Madrid all boast stronger squads than the Red Devils
The Red Devils got off to a good start in their group-stage campaign, beating Bayer Leverkusen 4-2, but the 50-year-old Scottish coach suspects that his side will struggle against Europe's elite.
"To win the Champions League you have to have five or six world-class players," Moyes told reporters after his side's surprise 2-1 Premier League loss to West Bromwich Albion on Saturday.
"If you look at Bayern Munich, they have five or six really world-class players and, to win it, you might have to have that in your squad.
"Look at Barcelona, who had it in the past, and Real Madrid have maybe got it now.
"That's the level you have to get at to win it. We've not got that yet. What we have got is experience and several players who are in that category or close to it."
United travel to Ukraine on Wednesday to face Shakhtar Donetsk in the second game of their Champions League group.