The 58-year-old Hammers boss was fined £8,000 and warned about his future conduct by the FA for questioning the integrity of the officials in his post-match comments following the game at Old Trafford.
He was unhappy at the awarding of a penalty to the home team while his side were denied two spot-kicks for what he felt were clear handballs.
Allardyce said he did not intend to suggest any bias in the officials but stood by his suggestion that they may be affected by large home crowds.
"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.
"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.
"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."
In the aftermath of the FA Cup game, 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."
He confirmed that he would not be appealing the fine.