Moyes' men take on Olympiacos in Greece on Tuesday in the first leg of their last 16 tie, and the Scot talked up his side's chances of claiming a fourth title come May.
"I see this as an opportunity to try and win the competition," he said.
"We have to go as far as we possibly can and win it, if possible. But we first have to get through this tie."
Despite indifferent domestic form, United have had a strong European campaign thus far, but Moyes acknowledged they faced a stiff test against an Olympiacos side that is sweeping all before them in the Greek Super League - currently sitting 20 points clear at the summit.
"I'm looking forward to the game, I really enjoy these games," he said.
"To win the group was an advantage. I'm looking forward to a really tough game against Olympiacos. We have to play well to qualify.
"Olympiacos have done very well against Paris Saint-Germain and Benfica. They came through a difficult group and are tough at home. It is a tough game."
Moyes confirmed that defensive duo Jonny Evans and Phil Jones had not travelled, but Wayne Rooney says he and his teammates come into the game in form and are harbouring ambitions of winning the competition.
"We've got the quality to go far," he said.
"The aim is to get a result. Of late, our performances have been good. We're playing well and we've improved and our form in the Champions League has been excellent so far.
"You normally need a bit of luck to go through but we have the quality in our team to go far, so hopefully we can do that.
"Every player wants to win trophies. I'm no different."
