Goals from Emmanuel Adebayor and Christian Eriksen had the visitors two goals in front at Old Trafford after 66 minutes.
Danny Welbeck pulled a goal immediately after Eriksen's header, however Moyes felt decisions went against his side as they went in search of an equaliser.
Ashley Young had claims for a penalty when challenged by Hugo Lloris and an apparent foul on Adnan Januzaj resulted in a booking for diving, something Moyes was not happy with.
"I thought the team played really well, (we) certainly should have had a penalty kick and a sending off for the challenge the goalkeeper (Hugo Lloris) had on Ashley Young," he said.
"Scandalous, it's a scandal, anywhere else on the pitch with your foot high and you follow through it would be a sending off.
"The goalkeeper comes out, Ashley Young gets the ball before him and he follows through, it’s an incredible decision that didn’t go our way, in fact it's probably one of the worst I've seen.
"That was a stonewall penalty kick, if that isn’t given as a penalty kick I don't think we're going to see one again in the Premier League.
"We didn’t finish well enough in the first half, we played well, especially in the first 30 minutes, but we got done a couple of counter attack goals. We just didn’t create the cross or the finish that might've got us the opening goal. We could have done better.
"All you can do is play well and hope you take the opportunities when they come. Their effort was terrific in trying to come back from 2-0 down. We didn't deserve to be behind. We'll keep trying to win the next game, that's all you can do."
Nemanja Vidic and Wayne Rooney both had chances to score in the closing minutes but found Lloris in good form, and United slipped to a third defeat in four at Old Trafford which saw them drop to seventh in the Premier League.
