Terry and his advisers will spend the international break deciding whether to appeal against his four-match ban.
The Chelsea captain has 14 days to make a decision and the publication of the full judgement by the FA regulatory commission appears to have diminished the likelihood of that happening.
Player's union chief executive Taylor has said Terry should accept his punishment and show remorse.
"Things have been said that shouldn't have been said," said Taylor. "We need reconciliation and if you're going to get reconciliation then people need to accept what they have done is wrong.
"Sometimes sorry is the hardest word, but it's a word that is very effective and it means a lot.
"Then we can move on. Without that, things continuing to fester. We need to move on - football has suffered enough, black players have suffered enough.
"It has caused division among black players and among white players. One of our banners is 'racism divides, let football unite' - that's what we need to do."
Taylor added that football should earn the right to its undoubted status as the number one sport on the planet.
"The game can't be so arrogant to ignore that there is no divine right to be the major spectator sport or participation sport in the world," he said.
"We have got to earn that and at the moment we have got a long way to go to earn that respect."
The commission described the Chelsea captain's defence as "improbable, implausible and contrived", adding that there was "no credible basis" for Terry's claim he had only been repeating words he thought QPR defender Ferdinand had accused him of saying during the match at Loftus Road last October.
It said they were satisfied the words "f****** black c***" were intended as an insult by Terry. The report stated: "There are further aspects of Mr Terry's defence that the commission finds improbable, implausible and contrived, and which serve to underline and reinforce our decision.
"The commission is quite satisfied, on the balance of probabilities, that there is no credible basis for Mr Terry's defence that his use of the words 'f****** black c***' were directed at Mr Ferdinand by way of forceful rejection and/or inquiry.
"Instead, we are quite satisfied, and find on the balance of probabilities, that the offending words were said by way of insult."
The commission said that character references from a number of people, including black players, made it clear that Terry was not racially prejudiced.
"It is accepted by everyone involved in the criminal and disciplinary proceedings that Mr Terry is not a racist," added the commission.
Terry had been cleared in Westminster magistrates' court in July of a racially-motivated public order offence.