Red Devils centre-half Phil Jones scored a second-half winner to ensure the defending Premier League champions remained unbeaten after booking their last-16 spot in the previous round.
United have endured a tough start to their domestic campaign following back-to-back Old Trafford losses, but Moyes hopes his side are handed a kind knockout stage draw next week.
I’m looking forward to taking those fans back to another final, and hope the draw is kind to us
“I think a club like Manchester United always has to be trying to win the trophy. The teams in this competition are very good, as everyone knows, but I think you need to get better as the tournament goes on,” Moyes told United’s website.
“Last year, I think a lot of people were surprised to see Borussia Dortmund and Bayern Munich get to the final, with no sign of the Spanish teams. I think it’s a tough competition, and it will be a hard one for us, but one where we will take every game as it comes and see how we get on.
“It’s a great tournament, all United supporters love it, they’ve been to finals before and know exactly what it means. I’m looking forward to taking those fans back to another final, and hope the draw is kind to us.”
MORE: Latest Man Utd news
MORE: Latest Arsenal news
MORE: The latest football news