The Reds' 3-2 aggregate win over Olympiacos on Wednesday night sent Moyes' men into the competition's quarter-finals, where many of Europe's other big guns now lie in wait.
And while United haven't always hit top gear this season – the Reds lie seventh in the Barclays Premier League – Moyes says there's no reason the team can't go on to lift the Champions League trophy in Lisbon this May.
“I hope so,” he told reporters at Old Trafford following the win over Olympiacos. “We will probably go into the quarter-final tie as underdogs but I don’t see why not [we can’t win the trophy].
“This football club is capable of it. If we play to our capabilities, which we've not shown that often this season, I think we can be a match for any team.
“This club has history in the competition. It knows what to do at this stage. We’re not shocked to be in the quarter-finals – it's something we do regularly. We will try to get into the last four now.”
When asked if Wednesday’s result could be the turning point for United this season Moyes was reluctant to be so bold but was nonetheless cautiously optimistic.
“I don't want to say this is the moment but in the same breath I really hope it is. It was a really good result in Europe as we came from 2-0 behind. We hadn't played well in