The Bosnian paid tribute to the head of the country's FA Mohamed Raouraoua, as well as his players and the national team's supporters, but was less than complimentary about the press when announcing his departure.
"I wish to pay tribute to the players and the technical, medical and administrative staff who gave me every assistance throughout this mission," he told reporters.
"The wonderful Algerian public wished me well since the day I first arrived and have remained loyal to me. I will always keep the fond memory of the extraordinary welcome they gave us on our return from the World Cup.
"The only sour note, which I want to confront, is the behaviour of certain - though thankfully not all - members of the press, who never ceased to stigmatise not only my work but also me and my family. I will never forget nor forgive that."
Halilhodzic, who guided the Desert Foxes to the last 16 of the World Cup, has been tipped to become the next manager of Turkish outfit Trabzonspor.