In a statement issued by his brothers, he said the trial had been an "attempt to use the court to intimidate and silence critical voices in the media".
Mr Greste said prosecutors had failed to produce any concrete evidence the three journalists had spread false news.
The seven-year jail terms handed to the trio sparked international outrage.
The White House said jailing journalists because their reporting did not fit the government "narrative" was "a blow to democratic pro-gress in Egypt".
Australia has said it will work to secure the release of Mr Greste, an Australian national and former BBC correspondent.
The statement appeared on a Facebook page called Free Peter Greste.
In it, he said: "Throughout this trial, the prosecutor has consistently failed to present a single piece of concrete evidence to support the outrageous allegations against us."
"At the same time, our lawyers have highlighted countless procedural errors, irregularities and abuses of due process that should have had the entire case thrown out of court many times over."
He pledged to do everything in his power to overturn the conviction.