West Ham threatened to halt United's title charge by twice going in front against the league leaders only to be twice pegged back.
Robin van Persie's late strike denied West Ham all three points, with replays suggesting the Holland striker was offside.
The decision angered Allardyce, who said a "famous victory" had been taken away from his men.
"The team has played the best they can play and they have scored one of the best goals of the season and the assistant referee takes it away from you," he told Sky Sports 2.
"It's a bit difficult to take, that's their job, it's their job to give the offside decisions that appear in front of them. This is a blatant one, this is not a position he should or shouldn't be in. He can see Van Persie is two yards offside, he should put his flag up, he doesn't.
"You could say if Manchester United hadn't have scored they might have scored from there on but to have to draw this game by a default goal from Manchester United it is a bitter pill to swallow.
"It's a fantastic performance by the team, outstanding performance in fact.
"They get rubbished some of our players for the type of football they play
because of me and I do think that's a disgrace because they have shown everybody how good they are today."