an eight-match ban for the same offence
against Patrice Evra last year but Suarez was found to have repeatedly used an abusive word when talking to the Manchester United defender.
Lord Triesman added: "Talking to many of the black players I got to know when I was chairman of the FA, a lot of them have been in touch and said, 'you kept saying there would be real progress [but] it doesn't look like it to us'.
"I think they feel a great sense of grievance - and they are entitled to because I don't think there is zero tolerance. And there isn't consistency in the sanctions either.
"All of these things - delays in hearing things, not dealing with it in a precise way, not dealing with it consistently - give the signal that it is not really at the top of the agenda."
Terry is due to decide whether to appeal against the guilty verdict but Lord Triesman, speaking at the Leaders in Football conference, said the verdict was the correct one and urged the defender to accept his punishment.
"He's within his rights to appeal. My own view is that it would be more sensible to apologise and accept it's not a good standard," said Lord Triesman, who
stood down as FA chairman in May 2010
following a newspaper article in which he was reported as suggesting Spain could drop its 2018 World Cup bid if rival bidder Russia helped bribe referees at the 2010 World Cup.
"I just don't believe in this day and age that anybody can think that it's OK, and that you don't owe an apology, not least to the other player."
Following the controversy over Terry, and over team-mate
Ashley Cole's tweet abusing the FA,
Triesman said it was time for clubs to include codes of conduct in players' contracts.
"What I think is important is for clubs to tell their very highly paid employees what general standards are expected of them on the pitch or in the training ground.
"Every club should set those standards and say, 'here's a set of standards we expect you to stick to'."
"Some clubs have done elements of it, but what hasn't happened is saying to people, 'what you've done off the field impacts on our brand', and that should have been said years ago," he said.
"Contracts have subsidiary documents of all kinds which get attached all the time, and I don't see any good reason why a general code of conduct in relation to people who are absolutely in the spotlight all the time should not be part of that."
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