Ferguson could face FA sanction
Ferguson felt the Red Devils were denied a penalty in the second half before Spurs equalised in stoppage time through Clint Dempsey to grab a deserved share of the spoils.
The controversial incident came just after the hour mark when Wayne Rooney, only introduced as a substitute moments earlier, appeared to tangle inside the box with Spurs defender Steven Caulker.
Beck remained unmoved by the challenge and Ferguson hit out at the assistant referee following the draw.
"It was a clear penalty," he said. "It was definitely a penalty. He has put his leg right in there.
"The linesman is facing it. I thought he had a very poor game, the linesman. I thought he was disappointing."
The 71-year-old went on to highlight a decision Beck made in favour of Chelsea in 2010, when he failed to flag Didier Drogba offside as the Blues won 2-1 at Old Trafford.
"We have got that history with him," said Ferguson. "He never gave offside with Drogba at Old Trafford when he was three yards offside.
"Everyone remembers that - I certainly do."
Ferguson, who had seen red-hot hitman Robin van Persie open the scoring for his side on a snowy Sunday in north London, also accused Beck of failing to spot a foul ahead of Spurs' dramatic equaliser.
"I thought Rafael was fouled actually in the build up to it," he said. "I thought it was a clear foul but we didn't get it.
"There was no way we were going to get a decision from the stand side linesman that's for sure."
Tottenham boss Andre Villas-Boas claimed his side were the better team and fully deserved their point, but is worried the debate over the penalty could eclipse his team's efforts.
"Obviously it is going to be debated and debated, and I hope it doesn't mar the game,'' he said.
"During the game we got most of the decisions against us. I prefer to look at this game on my view and United prefer to look at it on their view.
"We take our boost of confidence and the debate is going to be whether it was a penalty because that is controversy and it sells better, but we shouldn't mar the game and the quality of the game played in these difficult conditions."
The draw means United are now five points clear of reigning champions Manchester City, while Spurs sit four points behind Chelsea in fourth place.