The Serbian centre-back featured as the Red Devils earned a 2-0 victory against Everton at Old Trafford on Sunday afternoon, a result which stretched their lead at the summit to three points.
However, he was overlooked for Wednesday evening's game at the Santiago Bernabeu, with Jonny Evans and Rio Ferdinand preferred.
Sir Alex told Sky Sports: "We tried to manage Nemanja and Rio and if he had that extra day he would have been alright, but just three days after playing on a really heavy pitch at Old Trafford it was maybe a bit of a miss for us but I can't take a risk on a night like tonight."
The Scot went on to express hope that his side can show the defensive nous required in order to beat Jose Mourinho's men.
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"I think we have got attacking players, but obviously the roles that Michael Carrick and Phil Jones play are essential to how the game will pan out.
The 71-year-old also revealed just how much he is relishing the opportunity to face Los Blancos, declaring himself "lucky" to have been involved in so many big fixtures.
"Well, when I started as a coach I always dreamt of playing the Real Madrids, Barcelonas, Inter Milans and Juventus' and I've got that. I've been lucky. We've had some great European games over the years," he said.
"Tonight is two of the biggest clubs in the world, there's 200 million people watching on TV. That tells you just how the public view this game so you have got to look forward to it.
"There's a lot of nervousness inside me, but if my players can get to the levels I trust them to, they have a chance."