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 on Friday 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."
Allardyce reckons he should have been given the benefit of the doubt by the panel as he did not explicitly claim that Dowd, or anyone else, showed bias towards United.
"I thought we put an outstanding case forward and I thought I should have got the benefit of the doubt based on the fact I didn't say anyone was biased," he said.
"It is the implication that people might have thought I meant the referee was biased and that I may have thought it on my comments, and that was why I was fined. I tried to choose my words carefully and never mentioned that word (bias) whatsoever."
The 58-year-old also said he would not be looking to appeal the decision and his focus now turns to trying to secure another vital three points when he takes his Hammers side to struggling Aston Villa on Sunday.
West Ham have taken only eight points away from home this season and are the lowest away scorers in the division with just seven goals to their name.
It is something Allardyce is keen to rectify and believes scoring first in away matches is vital.
"Everyone knows the responsibility of turning around our away results, they must get better," he said.
"We have a fantastic opportunity to change the results we have had recently on Sunday given we had a big boost of confidence with a well-deserved win against Swansea last week.
"It is always a difficult task to win a game of football after going a goal down and it is obviously much more difficult when you're away from home.
"It is rare as a side playing in the Premier League for the first season to turn around a result after losing the first goal - we have to focus on the fact that we have to keep on a level playing field with Aston Villa and score the first goal if possible."
A third away win of the season could see West Ham return to the top half of the table by the end of the weekend with a potential gap of 12 points over the bottom three sides.