The manager concedes the Red Devils are likely to face a stern test when they travel to Ukraine and says he will be fielding a strong starting lineup.
The Red Devils travel to Ukraine on the back of two consecutive Premier League defeats following West Brom’s 2-1 win at Old Trafford on Saturday – the club's worst start to a campaign for 24 years.
Despite United winning its first Group A game 4-2 against Bayer Leverkusen, Moyes believes qualification will be harder than expected and says he will field a very competitive side at the Donbass Arena.
"I think we need to go there with a strong team. Going to Ukraine is tough because Donetsk have a good record," Moyes told The Mirror. "[The Champions League] has become a harder competition to win with the spending power of some of the big teams in other countries.
"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."
United failed to progress from its group two seasons ago, and Moyes wants to ensure nothing is taken for granted this time round.
Meanwhile, midfielder Anderson has offered his support to the manager, but concedes the club should be doing better this season.
"Everyone knows United have great players and even though the situation is not easy, we have to look ahead and think positive," he said.
"We want to win every competition we are involved in, so we need to focus now and move onto the next game. We have to show character."