"The big clubs look after their players as assets. There was no bold attitude from them, to say that they would not put up with it."
CNN asked the FA to respond to these accusations, but was told the ruling body would make no further comment on the Terry/Suarez cases.
Clarke agrees that clubs should not just look out for their own short-term interests.
"There has to be individual responsibility and accountability at the football clubs for the behavior of their employees," he said.
"There's an element of responsibility that needs to be addressed. The FA's sanctions for players, for entry-level discrimination, need to be far sterner."
The FA has said it will review its sanctions, but no changes can be implemented until the start of next season. Clarke's PFA said on Twitter this week that it had agreed to an FA proposal of five-match bans for racial abuse.
The Manchester incidents completely overshadowed Saturday's events at another EPL game hosted by Swansea, where a man was arrested and charged after Norwich defender Sebastien Bassong complained of being racially abused.
Norwich revealed later that police are investigating four cases of racial attacks on the Cameroon international in the past fortnight, three of them on social networking website Twitter.
Coming soon after two West Ham fans were arrested for alleged anti-Semitic abuse of Tottenham supporters last month, and several other troubling incidents this season, it doesn't paint a healthy picture of English football --- but shows the size of the challenge faced by the authorities.
Clarke said the question of suitable punishments requires an all-inclusive approach.
"It's easy for me to say a fan should get 'X' punishment, just as it's easy for a fan to say a player should get 'Y,' " he said.
"If we have some kind of consultation across the board to establish acceptable parameters or unacceptable behavior then we will be seen to be putting something into place that everyone has had an input in."
The FA is working with the British government to work out ways of dealing with football's problems, and Clarke says this will only be effective if there is a clear set of guidelines laid down for all areas of the game.
"The biggest change we need in football is some kind of protocol for issues that have come to pass over the past year," he said, when asked about club managers such as Kenny Dalglish and Andre Villas-Boas publicly defending their players Luis Suarez and John Terry while racism investigations were ongoing.
"We haven't got any definitive outlines on what should happen when there are incidents of discrimination, especially racial abuse. It's very much a gray area. The defenses go up at the club, they have their own brand and their own assets to protect.
"This is all before official investigation and procedure is taking place to ascertain whether that is valid support of the player or club. I think the first thing we need to do is to have a protocol where everyone knows exactly what should happen in these incidents, exactly what behaviors are expected of the people involved, of the club employees and of the press, as well."
He said the incident involving referee Mark Clattenburg, who was accused of racially abusing a Chelsea player before being cleared, showed both the improvements football has made and yet how far it still has to go.
"Procedurally it was a real step forward: something was claimed, it was reported, it was investigated and conclusion was drawn. I think that was outstanding, it was done promptly as well," he said.
"But because the whole issue went into the press and speculative domain instantly, there were questions that were being proffered and answered that people didn't really have the grounds to answer.
"A lot of speculation was drawn and it's possible and plausible that Mark Clattenburg's character had been tainted on the back of that. I believe we need a definitive outline on the protocol in such incidents."
It has emerged that the FA is considering cultural lessons for foreign players in order to prevent a repeat of the Suarez-Patrice Evra case last season, where the Liverpool striker was banned eight matches for constantly taunting the Manchester United defender with the term "negrito" during a match.
Liverpool's lawyers argued that it was an acceptable, and often affectionate, term in Suarez's native Uruguay -- but the FA ruled that it had much more negative connotations in Britain.