The publication of the disciplinary commission's full reasons behind Terry's four-match ban for racially abusing Anton Ferdinand also contained criticism of Ashley Cole for his evidence.
Cole responded with an offensive tweet aimed at the FA, for which he later apologised, and Professional Footballers' Association chief executive Taylor is concerned at the continuing effect on the game.
Terry has 14 days to decide whether to appeal, but Taylor questioned whether that would happen.
He told the Press Association: "The judgement is quite comprehensive and you get to the point when you wonder whether you just accept it and move on.
"This whole case is causing the game to implode.
"I would like the situation to be ended and for people to learn from it and move on with new focus, and new training programmes explaining clearly to players about what is racist and what is unacceptable.
"The has to be some reconciliation now because it is causing the game to implode."
Taylor welcomed Cole's apology after his outburst.
He said: "I would certainly approve and welcome that apology.
"Social media causes so many problems with people making comments and then finding them going public.
"Players are better off being more circumspect, considering what will happen if they do say something controversial."
He reiterated that the disciplinary process had dragged on far too long - it is now almost a year since the offence.
He added on Sky Sports News: "It's important the FA continues to grasp the nettle, although I would like the process to be speedier. The essence of justice is to deal with things quickly and transparently.
"For 12 months this has festered and only got worse. Progress has been undone and we have to apply ourselves even harder to ensure it doesn't happen again."