The Reds reduced Arsenal to just a handful of chances in the 90 minutes and might have snatched victory with an opportunity at the other end when Robin van Persie's header was brilliantly pushed onto the bar by the Gunners' goalkeeper Wojciech Szczesny.
Here's a transcript of what the United manager had to say to MUTV and BT Sport:
Solid defensive display
"It was a tight game, I think they [these fixtures] have been in the past. We won 1-0 at Old Trafford and it was tight. Both teams had opportunities but it ended up 0-0. I thought overall we looked quite compact and we defended well throughout the game and we had to do so. Overall defensively we looked sound and on the face of it we looked in control. I am happy because I think we played some good stuff, we were well organised and defended well. That was really important as when you come to Arsenal you've got to be hard to beat. You can't allow the small players to influence the game. In the main, we did that."
Van Persie chances
"I would like to have played better sometimes when we went forward. But we had opportunities to score, even from the first minute when Robin had a great chance. What a chance! I was out of my seat right away. He's got a great record against Arsenal so I was hoping for that one to go in.
"Then Robin had the one later on in the game when the keeper made a great save - I thought that might be the one. That was from a great bit of play and a great counter attack. Wayne's pass was