Made the difference
The Black Cats went into Saturday's clash at the Liberty Stadium hot in form with three win in their last four, but were humbled by Bob Bradley's side who climbed out of the relegation zone with the three points.
Fernando Llorente scored a brace, but it was opening goal from Gylfi Sigurdsson's opener from the spot that Moyes had a gripe with. Wayne Routledge's cross was blocked by the arm of Jason Denayer who was facing the opposite direction, and Moyes admitted that Craig Pawson's decision changed the game.
"I'm frustrated we didn't play well enough," he told Sky Sports. "Swansea deserved the victory in the end but it turned on a big decision for me."
The Scot continued, "There was very little in the game and these games are so important. Whoever gets the first goal it can make a big difference and I'm not convinced it is the right decision. It did turn the game."
Moyes added, "My view of it was he goes to block it. He is not looking at the ball he has no intention. He is two yards away from the ball - very difficult - so I think it is the wrong decision."
Going to be tight
It is a bump in the road of what has been a good couple of weeks for the Wearsiders, but still have some crucial matches coming up over the festive period.
"That's the way it goes so everybody knows the situation," said Moyes. "We've been on a good run. We didn't play as well today as what we have done but nevertheless that is the way the league is."
He explained, "We won the other week 3-0 against Hull at home. Swansea today have beaten us 3-0 and it is going to be tight around that end of the league."
Moyes added, "We've got to show it is and next time we play again we show what we can do. Look, we are improving. Six weeks ago you would have said we were written off but we are back in it."
Moyes concluded: "What matters is where we are come May but we are certainly back in with a fighting chance."
Sunderland AFC will take on Chelsea at the Stadium of Light on Wednesday, December 14 with kick-off at 8pm GMT.