United kicked off the group stage campaign with an impressive 4-2 victory over Bayer Leverkusen earlier this month. The next Group A test comes at the Donbass Arena in Ukraine next week and Moyes is expecting a challenging encounter.
"I think we need to go there with a strong team. Going to Ukraine is tough because Donetsk have had a good record," he told reporters on Friday. "I know they’ve sold one or two players but they have five or six Brazilians; they are not all Ukraine-based players but from all over the place.
"Bayer Leverkusen was fantastic and I’m really looking forward to Wednesday and seeing what it’s like getting to be involved in these competitions. I think the history here is to be known throughout Europe; Manchester United and their history shows you that has been the case.
“It has become a harder competition to win with the spending power of some of the big teams in other countries," added the United boss. "With the emergence of all the good Spanish players and Spanish teams and now you have PSG... the competition has become much more open than it was in years gone by.
“It’s been hard for Manchester United as well and progress is not something that is guaranteed. There were no guarantees for Manchester City last year. You have to play well enough and grow into it and, hopefully, keep moving along."