United claimed their first win in the league at home since January as goals from Juan Mata, Chicharito and two from Wayne Rooney ensured the hosts would come from behind to defeat Paul Lambert's side at Old Trafford.
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"At the start if you said we'd get to the quarters then great but we want to be in the semi-final and then the final. But we've got a big tough game against probably the best side around. But bring the challenge on and coming to old Trafford is not easy for any side.
"I've been saying all the time I've been here the crowd have been great. We didn't start well but the crowd were great. Every fan I bump into they tell me they know exactly what it's like at Man United.
"The fourth goal is the type I've been looking to score. Adnan [Januzaj] weaving away and it was a great cross. You want to be excited by the football you see and the fourth goal excited me."
On Rooney, Moyes added: "He's a top player and he's been great since the start of the season. I said after the game if you keep scoring two goals a game then it's going to give us a great chance of doing much better. His form and the way he's playing has been great."
Moyes also hailed Mata's performance after the playmaker scored his first goal for the club since becoming the club's record signing after joining from Chelsea in January. He continued: "Everyone knows what he's capable of but he needed a goal because it's a big part of his game and it's a reason we signed him because he scores goals.
"He's been instrumental in a lot of our good play and I think he's played really well in recent weeks.
"I took over from Sir Alex a great team who were champions. But we need to add to it. All the players I seem to talk to are really keen to join Manchester United let's hope it comes to fruition in the summer time."