Allardyce was upset that assistant referee Harry Lennard has failed to spot Robin van Persie was offside when he scored United's second equaliser of the game and claimed it had cost the Hammers a "famous win".
There was a suggestion the 58-year-old may have had to explain his comments to the FA but the governing body has confirmed to Press Association Sport it will not be pursuing a disciplinary case.
After seeing his side take the lead twice against the Barclays Premier League leaders Allardyce questioned the level of officiating and feels more should be done to improve the overall standard of referees and their assistants.
"I think it is a big decision that has possibly taken the famous victory away from us," he said immediately after the match.
"To play as well as we did today and score the types of goals we scored - when you see it is an offside goal that is bitterly disappointing.
"This level of football has to be equalled by the level of the officials who are in charge of the game.
"His [Lennard's] coaches have to coach him properly and coach him into getting better - that is why they are professional these days.
"They need coaching on the good decisions, with a pat on the back, but also they need coaching on when they haven't made the right call. It is a major decision that has gone against us."
Allardyce has already landed himself in hot water with the FA this season, coincidentally after an FA Cup tie against United. The former Blackburn boss was fined £8,000 back in February for suggesting United had gained from home advantage after the Red Devils won their third-round replay against West Ham 1-0.