The Reds star was hit with a 10-game ban for sinking his teeth into the Serbian on Sunday. The club had fined him and indicated that they would accept a punishment from the Football Association but have reacted with shock at the length of the suspension.
Asked by reporters if he had been let down by Suarez, Rodgers replied: "No, not at all. I believe if I had half a dozen more players with a similar mentality then we would be in a different position as a football club.
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"But that doesn't mean he should be thrown to the garbage, which is what has happened with a lot of people in these last couple of days, and it's certainly something I won't be prepared to do.
"He's a boy that's working tirelessly, him and his family, to fit in to the life and the way it is in this country, and unfortunately for him he's made a mistake and he's got a sanction that I don't believe fits what he did."
Liverpool goalkeeper Pepe Reina blasted the FA on Thursday for what he sees as different treatment for Suarez because of his Uruguayan background or personal history and Rodgers agreed that the ban seemed to be targeting the striker specifically.
"For me, I can't help but look at it, and look at the sanction that's been put on Luis for the incident, and I honestly feel that the punishment has been against the man, rather than the incident," he argued.
"I think of course there was a lot of euphoria around the time it happened but whenever you come away from it and you look at the cold light of day and assess it, then it's violent conduct.
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"Maybe you need a bit of help. The player needs a bit of help and that's something we'll look to provide here as a football club and our supporters and our city - and something that I would expect any football club or business to do."
When questioned as to whether Suarez might have a specific psychological issue, Rodgers insisted: "No. What I'm saying is, is in modern life, whether you're a football player, a plumber, a joiner, a bricklayer, you work in a warehouse, you're not immune to your issues and problems, especially if you're a footballer.
"Because you might have a bit more money than someone else, it doesn't rule out that sometimes there might be something clinical that is wrong with someone.
"All we're saying is that whatever the issue is - the behavioural issue - we will do everything we can to support that person and that person now is Luis Suarez."