Chelsea captain Terry was handed the suspension and a ?220,000 fine after being found guilty of using a racist slur towards Anton Ferdinand by an independent FA regulatory commission. The ban was half of that meted out to Liverpool striker Luis Suarez for racially abusing Manchester United defender Patrice Evra.
The FA commission said Terry had been given a lesser ban because the "racist insult was issued only once", as opposed to repeated use by Suarez. But Lord Triesman told the BBC: "It may be when you look at all the detail they thought there were reasons for [it]. I can't see it."
Terry is due to decide during the international break whether to appeal his guilty verdict.
Lord Triesman added: "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. I just don't believe in this day and age that anybody can think that it's okay, and that you don't owe an apology, not least to the other player."
The fallout from the Terry verdict saw Chelsea team-mate Ashley Cole launch a foul-mouthed Twitter tirade at the FA, something which saw him charged with misconduct on Monday.
English football's governing body announced on Tuesday they were set to introduce a code of conduct for England players and Lord Triesman, who was their chairman between 2008 and 2010, wants something similar included in contracts at club level.
He said: "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'."
He added: "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.
"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."
Source: PA
Source: PA