The ex-England boss thinks the current head coach should have kept quiet until a decision was made, while Football Against Racism's chief also criticised the manager's commentsEngland manager Graham Taylor has revealed that he was surprised by Roy Hodgson's public support of John Terry, with the FA currently probing into alleged racial abuse by the player.
The Chelsea defender has been cleared in court of allegedly using racially abusive language towards Anton Ferdinand of QPR, but the FA have re-launched their own investigation into the incident.
The current Three Lions boss, who has already insisted Terry's international career is not over, has now indicated that he hopes the Blues' man will be cleared once more, despite the new inquiry being held by his employers.
Taylor admitted he was shocked by the former West Brom manager's decision to talk openly about the case, stating his belief that Hodgson shouldn't have commented until a conclusion is found.
"I was surprised that Roy said that," Taylor told the BBC.
"He shouldn't be getting involved in any comment on that until a decision [by the FA] has been made. I don't think it was a good thing for him."
The England head coach has also come under criticism from awareness group Football Against Racism due to his support of Terry.
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Piara Powar, executive director of the organisation, was unhappy that Hodgson, who works for the FA, spoke in favour of a party concerned by an ongoing investigation, suggesting it brings the governing body's impartiality into question.
Powar said: "Hodgson's comments on Terry are foolish. It is not helpful to the process the FA has undertaken in any way.
"The England manager is employed by the FA, who have a dual role in running the national team and being the governing body. Whatever support Roy Hodgson wants to give to a member of his squad, he also has to remember the FA's wider role.
"For the England coach to go public with his view like this calls into question that dual function."
Due to the case first being investigated by the police, and therefore the FA being unable to intervene, the defender's second hearing will take place 11 months after the incident.
Powar insisted the length does not matter as long as the final decision is correct, adding: "My primary concern with this case is that justice is done. That comes above any expediency within the decision-making process.
"There has been a criminal case involved here and no doubt the FA are carrying out their own investigations.
"What might have been better was if the FA put out a statement explaining what was happening and how long it was likely to take because the way it is going on, it risks people getting fed up with the situation."
Powar suggested one area of the justice system that could be improved is determining who exactly should be punishing players, citing a case where Emmanuel Frimpong was first warned by his club over an offensive tweet, before being fined by the FA at a later date.
He said: "I accept these are complex matters but when you looked at Frimpong's 'Yids statement', which clearly in the context it was used was derogatory and racist, first his club stepped in, then the FA took action as well.
"These players are employed by their clubs, so that is another issue that needs looking at."