The Uruguay striker was retrospectively suspended for nine international games and banned from all football-related activity for four months after video evidence appeared to show him sinking his teeth into the shoulder of Italy defender Chiellini during Tuesday's Group D game in Natal.
That represented the third occasion Suarez has been reprimanded for biting, the other two incidents having come at club level for Ajax and Liverpool respectively.
However, he maintained his innocence, claiming there was nothing untoward about his actions in a statement sent to FIFA.
He said: "At that moment of impact, it forced me to bend my knees and lose balance and I ended up falling on the opponent (Chiellini).
"I slammed my face against the player, leaving a small bruise and sharp pain in the teeth - therefore the referee stopped the game.
"That is what happened and in no case what has been described as a bite or attempting to bite happened."
Suarez left Brazil after receiving his punishment, which Uruguay have confirmed they will appeal, and has been greeeted by widespread support in his homeland.
In a separate statement, he said: "I write this post to give thanks to the outpouring of support and love I am receiving. Both myself and my family really appreciate it.
"Thank you very much for being by my side."
Uruguay continue their World Cup campaign on Saturday with a last-16 tie against Colombia.
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