Suarez's ban for biting an opponent while playing at the World Cup for Uruguay means he would miss 13 matches for Liverpool between the start of the season and the end of October. He is also banned for nine international games and has been fined 100,000 Swiss francs (£66,000).
Suarez's lawyer has described the sanctions as "grotesque and absurd" and added that "all that was missing was life imprisonment".
Valcke, FIFA's secretary general, told a news conference in Rio that the ban reflected the "unacceptable" behaviour on the world stage and that the 27-year-old should "seek treatment" as it was his third biting offence. Liverpool are taking legal advice over the case but Valcke claimed the worldwide ban was correct.
He said: "It's not Liverpool who is punished. It's the player who is punished.
"What happened with Suarez was far beyond the fair play and the attitude you should have when you play at the World Cup.
"When you are with the 32 teams among 23 players in each team you have to show the best of the best as they are the example for the rest of the world.
"I applaud the decision which was made by the committee to sanction the player in this way because what he did is unacceptable and not the image we want to give to the world."
Valcke added: "I think he should find a way to stop doing it. He should go through a treatment and find something, it is definitely wrong.
"It is more than one incident that's why it has to be exemplary."
Suarez's victim Italy's Giorgio Chiellini has said the punishment was "excessive" but Valcke insisted it was proportionate.
He said: "You will always find someone who will say it is excessive - so what? They are decisions made by the disciplinary committee based on what has been seen by hundreds of millions of people. It is not what you want your kids, the little ones playing football around the world to see at the World Cup.
"That's not what you do at any level of football or in life."
The international players' union FIFPro has questioned why Liverpool should be affected by the ban and said FIFA should have included treatment and rehabilitation as part of the sanction.
An appeal is being lodged against the decision and Suarez's lawyer Alejandro Balbi said they would take the case all the way to the Court of Arbitration for Sport (CAS) and that he remained in constant contact with Liverpool.
He told Spanish radio station Cadena Cope: "The ban is absolutely disproportionate considering what Luis did.
"Julio Grondona, vice-president of FIFA, told me that he had never seen such a serious ban handed to a player.
"This is so grotesque and absurd that the CAS will have to revoke this unjust ruling.
"Unjust not just due to the number of games given, which is already incredible, illogical and arbitrary, but also the issue of not being able to be allowed to have any relationship with football in 120 days, and then there's the fine. All that was missing was life imprisonment.
"We are in constant contact with Liverpool and we are ready to fight until the end."
Betting website 888poker announced on Thursday that it had ended its arrangement with Suarez following the incident, a decision Balbi described as "madness".
Chiellini has expressed his sympathy for Suarez, and said in a statement on his website the punishment was "excessive" adding: "At the moment my only thought is for Luis and his family, because they will face a very difficult time."
Suarez has left Uruguay's national team in Brazil and returned home to Montevideo.
Liverpool are working their way through the legal minefield of the four-month ban but are still a long way from even considering launching a challenge to FIFA.
The club have dismissed claims by Balbi that their representatives are meeting with him and the player's agent Pere Guardiola in Barcelona on Friday.
FIFA has confirmed the ban would not prevent Suarez being transferred to another club.
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