Taylor, chief executive of the Professional Footballers' Association, said the delay had caused the issue to "fester" within football.
Chelsea centre-back Terry was banned for four matches on Thursday for using racist language towards QPR defender Anton Ferdinand in October last year and Taylor called for the game to move on and to continue to eradicate racism.
Taylor said: "Almost 12 months on and the John Terry case was still not heard by the FA until the day after Luis Suarez shook hands with Patrice Evra at Anfield.
"Such a delay has allowed the matter to fester and cause divisions in the football family which will take a long time to heal - if they ever do.
"We have to move on now and move on together and continue our focus to eradicate racism from the game and society.
"There should be new educational processes for all players - young and old, and for managers and directors.
"There should be equitable recruitment processes, and a fast-track disciplinary process that does not allow for delays or holding off at the request of the Crown Prosecution Service."
The FA had delayed their own disciplinary hearing until after the magistrates court case - where Terry was acquitted - at the request of the CPS.
A PFA statement read: "The time it has taken for a decision to be reached in this case, nearly 12 months, has benefited no one.
"We will be speaking with The FA to seek changes to their disciplinary processes to ensure cases are heard more quickly.
"The time this has taken has caused a lot of issues including, for example, international selection and captaincy, respect for opponents and the image of the game.
"We must therefore work together to ensure that matters such as these are dealt with as expeditiously as possible.
"It is important that any sanction is served as close as possible to the original offence to avoid situations festering and greater resentment building up."
Terry quit the England team on Sunday, claiming his position had been made "untenable" by the FA continuing to pursue him despite that previous not guilty verdict.
The issue of racism has also been pushed back to the forefront of the English game, with the PFA vowing to redouble their efforts to ensure progress continues to be made.
"We believe that through many of our initiatives progress has been made and the huge level of publicity for these recent cases shows the importance of these issues in this country," said the PFA.
"Our Government has recognised that football has been at the forefront of anti-racism campaigns and has achieved much success.
"This is an opportunity for football to demonstrate going forward that it can deal with such issues if they arise, recognising that penalties are significantly higher than would apply in the Courts.
"We have to move on now and move on together by reiterating our full support for all anti-racism initiatives.
"We need to focus on education for players, managers, owners, administrators and supporters. We also need to look at equitable recruitment policies.
"We must put in place additional support for players to feel comfortable in reporting incidents of racism. Thereafter, a streamlined fast track disciplinary process which the players have trust in to deliver fair decisions and appropriate sanctions if racist behaviour is proven.
"By doing this, football will continue to show its ability to deal with this problem which can divide our game and society in general."