The manager was delighted with the way the champions maintained composure, despite losing an early goal, to find a way back into the game thanks to two wonderful Adnan Januzaj strikes.
Moyes told MUTV: “I was pleased with the reaction of my players to going 1-0 down. I didn’t think we deserved to be 1-0 down, albeit we could have been 2-0 down at one point if it wasn’t for a wonder save from David De Gea.
"I thought we made a real mistake to give them a goal but I thought after that we controlled most of the game, albeit I didn’t think we forged enough chances. We had lots of crosses and balls into the box but nothing really which was telling enough to get us a goal."
Although the manager admitted he would like his team "to have scored a few more goals," he felt the outcome was still a fair reflection of how Saturday's game panned out.
“I thought today’s performance merited a victory," said Moyes. "That was an important thing for me. I thought we merited it. We played with more speed and there was a better intensity to our game."