The Hammers led on two occasions at Upton Park before Robin van Persie levelled in the 77th minute, with the goal standing despite the Dutchman being offside in the build-up.
van Persie slotted home after Shinji Kagawa's initial attempt had deflected back off the woodwork but Allardyce suggests he should have been flagged for being in an offside position when clinically putting the ball in the back of the net.
"The team has played the best they can play and they have scored one of the best goals of the season (through Mo Diame) 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."
The Hammers boss continued: "Andy Carroll has a shot two minutes in and his flag went straight up so I don't know what's going on.
"This has taken a famous victory away from us today. To draw this game by a default goal from Manchester United is difficult to swallow. A fantastic performance by the team - they get rubbished for some of the football they play and that's a disgrace as well.
"They (officials) shouldn't make those mistakes. If we (players) make those mistakes they're out, dropped and they're blatant. If you make big decisions and don't get them right you're out of the team. It was an offside goal and it shouldn't have been given."