Lord Herman Ouseley indicated David Cameron should have pressured the FA to draw up a clear process for punishment instead of speaking out against the South American
The 26-year-old was handed the lengthy suspension for biting Chelsea defender Branislav Ivanovic during a match on Sunday, but the decision has been criticised for being inconsistent with past punishments.
And Lord Ouseley has indicated Cameron's call to make an example of the Uruguayan may have influenced the commission, while insisting he could have instead pressured the FA to be clearer on this kind of issue.
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"Isn't justice supposed to be administered through proper process? Without the Prime Minister being involved? Without the most senior politician in the country trying to influence the outcome of what should be an independent process?
"What the Prime Minister could and should have been saying was that the Football Association have a responsibility to sort out these matters, so that there is a clear process where everyone understands what the penalties are."
Lord Ouseley then compared the Suarez case with Blues defender John Terry's criminal case and FA charge for racial abuse, where the England international was acquitted by the courts, but banned for four games by English football's governing body.
Ouseley insists Cameron was quiet on the issue, adding: "I didn't hear the Prime Minister intervene in John Terry's case, saying: 'The captain of England has shamed England'."
The Kick It Out chairman then added his own support to recent calls for a clear set of rules and punishments for different offences.
"You have got to have a tariff," he said.
"It is a ludicrous situation, because if you've committed an offence – let's say it's the Suarez one and you've bitten someone – you should know that this is going to be a specific sentence, if found guilty."