United qualified from their group as winners after the 1-0 win over Shakhtar Donetsk, and Moyes claimed that his team are good enough to win the competition.
"A club like Manchester United has to always try and win a tournament like [the Champions League]," Moyes told ITV Sport.
"We're in this competition and we're a very good team. Everyone knows that it is tough, but it is one we're in and we'll see how we get on.
"As a club we could be considered one of the favourites, but as a team we have to improve if we are going to keep progressing. Hopefully we have given ourselves the best chance by winning the group."
The victory was their first for four games.