Sunderland took the lead when 40-year-old United veteran Ryan Giggs inadvertently bundled the ball into his own net just before halftime when under pressure from Phil Bardsley.
Nemanja Vidic headed United level seven minutes into the second half before — according to Moyes — United was thwarted by a poor decision by referee Andre Marriner in awarding the penalty.
"I feel we are having to play the opposition and the officials at this moment in time," Moyes said on United's in-house television station.
"Maybe I've got to understand that's what happens at Man United. But if we do, we certainly aren't getting much in our favor at this moment in time."
The outlook isn't completely bleak for the Scot, with his team still in the Champions League and facing Olympiakos in the round of 16 next month.
The 72-year-old Ferguson continues to loom large over his successor, watching at the Stadium of Light in his role as a United director on another miserable night for the club he managed for more than 26 trophy-laden years.
With Robin van Persie and Wayne Rooney injured, Moyes was relying on Danny Welbeck for goals. However, the striker was shackled by a defense including former United defenders Wes Brown and John O'Shea. "If we can get them (Van Persie and Rooney) back for the second leg that would be great," Moyes said. United was the first team to have the ball in the net, but Adnan Januzaj's effort was ruled out on the ground where he scored twice on his debut in October because Giggs was adjudged to be in an offside position.
Sunderland sprang into life as the first half was ending, with Bardsley driving a low shot at United goalkeeper David de Gea before the hosts went in front.
Seb Larsson whipped in a free kick that was met at the far post by Brown, who squared the ball across the goalmouth before Giggs turned it into his own net.
