Allardyce was fined £8,000 and was warned about his future conduct for post-match media comments which the FA claimed questioned the integrity of officials or implied that they were motivated by bias.
Allardyce was unhappy that Manchester United had been awarded a penalty while his side were denied spot-kicks in relation to two handball incidents.
At the time Allardyce said: "You see it time and time again at Old Trafford.
"There's no doubt about the difference between Rafael's handball and Jordan Spence's. Spence plays for West Ham and the away team, while Rafael plays for the home side at Old Trafford."
Allardyce today claimed his comments did not suggest referee Phil Dowd or any of the other officials involved in the 1-0 defeat were biased towards United but felt he was right in his comments about people being influenced by big crowds in big stadiums.
"For me I spoke the truth, so if you like I have been fined for speaking the truth, but there you go, we move on," he said.
"What I had to do was present my case and give it to the panel and make sure they understood what I meant and there was no doubt I meant nothing other than the influence that happens at the big arenas that happens to everyone when you go there.
"Those influences can make people make decisions that are right or wrong, not just Phil Dowd but players and you as a manager."
West Ham last week