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.
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."
