FIFA had made a "scapegoat" of Suarez and had "punished him with excessive severity" but the forward will have the full support of the Uruguayan football authorities, Tabarez told reporters on Friday.
He refused to answer questions at a packed news conference the day before his team face Colombia in their World Cup last-16 match at the Maracana, and after reading from a prepared statement for over 14 minutes left to loud applause from Uruguayan reporters.
Suarez was banned on Thursday for Uruguay's next nine competitive international matches and from any involvement in football for four months after biting defender Giorgio Chiellini in their 1-0 Group D win over Italy.
Tabarez said after seeing the images of what happened, he and his coaching staff expected action to be taken against both Suarez and Chiellini.
"But we never thought the decision would be what it was and of such an excessive severity," he said.
"It was a decision much more focused on the opinions of the media who at the conclusion of the match, and at the press conference afterwards focused on just one topic.
"I don't know what their nationality was - but they all spoke English."
Tabarez hinted that some kind of conspiracy theory was at work to determine Suarez's punishment.
"When I speak of media attacks the topic that was concentrated on was the background and history of things that have happened in the past," he said.
"We know that he was sanctioned, he was punished, and he complied with those sanctions but in spite of that the harassments have continued."
Tabarez then turned his attention to FIFA.
"We all know where the power lies - in the hands of the organiser," he said.
"But that does not mean we will accept the indiscriminate use of that power. I am talking about the Disciplinary Committee that imparts justice.
"I have also been a teacher in my life and a professor and I am presenting the theory of the scapegoat, and there is a danger in proceeding this way.
"The scapegoat is a person with rights and in the case of Luis Suarez here is a man has made mistakes and has faults but who has made a significant contribution on the pitch.
"But with this decision, who wins? Who is the winner? Who loses? Who benefits? Who has ended up getting things their way?
"I cannot give you the final answer but not all cases are judged the same."
He then seemed to accept that Suarez had done something wrong.
"I am not justifying anything and saying there should be no punishment," he said. "I don't, though, agree with the theory of having a scapegoat."
Before leaving Tabarez said he would be resigning from his positions with FIFA where he has sat on both the Strategy Committee and the Technical Study Group.
"I have been linked with FIFA for many years as a member of the TSG and as a teacher and I have a position now on the Strategy Committee, but I now feel I must leave that position," he said.
"It is not wise or prudent to be in an organization with people who have values very different from those I believe in."
Before walking out without saying a word about Saturday's match, he said Suarez would have the full support of the Uruguayan people and football authorities.
"To Luis Suarez the person who has always co-existed with us, he is on the path to be better and he will never be alone in that attempt."
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