United ended a frustrating week, which saw them beaten 3-0 by neighbours Manchester City on Tuesday, in fine fashion by beating Aston Villa 4-1 in the Premier League at Old Trafford on Saturday.
The champions' hopes of securing a top-four spot are all-but gone, though the win over Paul Lambert's side was a timely boost ahead of Tuesday's UEFA Champions League quarter-final clash with Bayern Munich.
And, despite a place at European football's top table looking beyond them next season, Moyes insists players are still desperate to move to Old Trafford
"When I came in I knew what the task was going to be," he told BT Sport.
"We've got to build a team. I've already got a great team, they were the champions under Sir Alex, we're looking to add to it.
"All the players I talk to are keen to join Manchester United so hopefully that comes to fruition in the summer."
Much of the game's build-up had been dominated by a planned protest against Moyes' management of the struggling champions, with a plane trailing the message 'Wrong One - Moyes Out' flown above Old Trafford during the contest.
But the former Everton boss was given great backing in the stadium and he has now turned his attention to facing the European and Bundesliga champions.
He added: "I'm really looking forward to it.
"It's the quarter-final of the Champions League. We said at the start if we get there, great.
"We want to be in the semi-final and final. We've got probably the best team in Europe at the moment but bring it on, it’s not easy to come to Old Trafford."
