Moyes, under pressure after losing his third consecutive game in all competitions, pointed the finger at referee Andre Marriner, who he criticised for awarding a free kick that led to Sunderland's opening goal.
The referee also had a decisive hand in Sunderland's winner, pointing to the penalty spot in the second half after Adam Johnson had been felled by Tom Cleverley, allowing Fabio Borini to smash the spot kick into the roof of the net.
"It is difficult we just need to keep going," Moyes told Sky Sports. "We didn't do a lot wrong. I thought the referee was going to blow in our direction for (the free kick that led to) the first goal. I couldn't believe he gave (Sunderland) a free kick. It was a terrible decision.
"We are all just laughing at them (the officials) at the minute.
"It looks as though we are having to play them (officials) as well as the opposition at the moment."
United, who were knocked out of the FA Cup by Swansea City on Sunday and beaten by Tottenham Hotspur in the Premier League on New Years' Day, have endured a miserable start to the campaign under Moyes.
With the club seventh in the Premier League and 11 points behind leaders Arsenal, the League Cup had taken on added significance as Moyes's most likely route to silverware.
He remains confident of getting a result in the second leg on Jan. 22, to tee up a likely final against local rivals Manchester City who play West Ham United in the other semi-final.
"I thought the players, our crowd were unbelievable, the players deserved to get a result," he added. "It's a two legged game and I am really looking forward to the second leg."