The Reds had claims for a penalty turned away by in the second half, after Tom Cleverley's effort appeared to strike Frank Lampard's arm. Match referee Martin Atkinson declined to award a spot-kick, leaving Moyes to call for clarification of the rules after the game.
"I think that’s two penalty decisions in a week against Chelsea which have been good shouts," said the United manager. "I thought the referee gave a handball on Oscar about five minutes later which was less of a handball than the one in the box, so I think it could do with getting cleared up.
"I don’t think the managers are quite sure of what is and what isn’t a handball. I think the referee had a good game, but it was a big call for a penalty kick in a game like this."
As for reflections on his first competitive match at Old Trafford as the home boss, Moyes said: "I'm extremely proud to be managing Manchester United and I was very happy with the reception I got. But I want to be applauded in the future for winning things."