The Scot was furious with the award of a free kick in the build-up to Sunderland's first goal but says he is looking forward to the second leg at Old Trafford
The Red Devils went behind thanks to a Ryan Giggs own goal before Nemanja Vidic equalised just after half-time in the first leg of their Capital One Cup semi-final.
However, the hosts were awarded a penalty after Tom Cleverley felled Adam Johnson with Fabio Borini converting from the spot to seal the win.
Speaking after the game, the United boss criticised the officials and said his team did not deserve to lose at the Stadium of Light.
"It is difficult we just need to keep going," he told reporters. "We didn't do a lot wrong. I thought the referee was going to blow in our direction for the first goal. I couldn't believe he gave a free kick. It was a terrible decision.
"We are all just laughing at them at the minute. We get a player booked for doing the same. It looks as though we are having to play them [officials] as well as the opposition at the moment.
"I thought the players, our crowd were unbelievable, the players deserved to get a result. It's a two legged game and I am really looking forward to the second leg."
Moyes also took time out to praise the travelling supporters and says he can understand their frustrations after watching the team lose for a third consecutive match.
"They were brilliant tonight and I would like to thank them all. They supported me and the team," he added.
"The fans know we’re going through a difficult time and have probably not seen it as bad as this for a long time.
"But I’m determined to put it right and I’m sure we will. I sense that [determination] in the dressing room as well."
The second leg of the Capital One Cup semi-final takes place at Old Trafford on Wednesday 22 January.