United have lost three of their opening six games in the Premier League under Moyes, with the latest setback coming in a 2-1 home defeat to West Brom at Old Trafford on Saturday.
The Premier League champions were unsuccessful in their pursuit of a number of summer transfer targets, with interest in Cesc Fabregas, Leighton Baines and, finally, Ander Herrera all coming to nothing, and Moyes is concerned that his squad may lack the quality to challenge for Europe's top club prize.
"To win the Champions League, you need five or six world-class players," he told several national newspapers.
"Look at Bayern Munich, they have it. Look at Barcelona, who had it in the past and Real Madrid, who have maybe got it now. That's the level you have to be at to win it. We've not got that yet but what we have got is experience."
The Red Devils began their Champions League campaign with a 4-2 home win over Bayer Leverkusen earlier this month and face a difficult assignment away to Shakhtar Donetsk on Wednesday.
They have not enjoyed great success in either of their previous two European campaigns under former boss Sir Alex Ferguson, going out at the group stage in 2012 and losing in the last 16 to Real Madrid last season.
Domestically, United's start to the campaign is their worst since the 1989-90 season - one which ended with Ferguson's first silverware as the club won the FA Cup.
The defeat to West Brom was their first home loss to the Baggies since 1978.