"He was not fit enough for a game of that standard," said Ferguson. "The pace of the game demanded a referee who was fit.
"It is an indictment of our game. You see referees abroad who are as fit as butcher's dogs.
"We have some who are fit. He wasn't fit," he was quoted as saying on the Sky Sports website.
"He was taking 30 seconds to book a player. He was needing a rest. It was ridiculous," added Ferguson after champions United went one point clear at the top of the Premier League ahead of Chelsea who host Liverpool on Sunday.
Sunderland twice led through Darren Bent and Kenwyne Jones but United fought back through Dimitar Berbatov and an injury-time own goal from defender Anton Ferdinand.
"We rescued a game in which we played so badly," Ferguson told United's in-house television channel. "Our passing was just not what I expect of the team.
"We continued to give the ball away repeatedly... but credit to the players, they never give in. It's a good quality to have.
"We've got something out of the game on a day when we've played really badly," he added.
Sunderland manager Steve Bruce said it was agonising to concede such a late goal.
"You'll always take a point at Old Trafford but it is disappointing to concede a goal so late and it feels like we've been beaten," said the former United defender.
"We just needed a little more luck to hang on."
