The team returned to their Durban base straight after Saturday's 2-0 defeat in Port Elizabeth and, with matches against Nigeria and Argentina to come, the mood in the camp on Sunday was as miserable as the weather on the Natal coast was glorious.
Although the defeat left the 2004 European champions still without a win or a goal in two World Cup campaigns, Tzorvas said a storm of domestic criticism would not help.
"We must not forget who we are and what we can do. It's not nice to hear criticism. Let us just enjoy World Cup 2010," he told reporters after training at a school in the north Durban suburbs.
"There's no need to be critical, just be calm and let us see what we can do."
Greece supporters are already calling for the head of septuagenarian German coach Otto Rehhagel but Tzorvas said the players were still behind the architect of the Euro 2004 triumph.
"I have the best opinion of this coach," he said. "He is the chief and general of this team and I respect him a lot."
The squad spent the first 10 minutes of Sunday's training session on a warm, sunny morning stood in a circle listening to Rehhagel's assistant issue a rallying cry.
"We're just trying to regroup after the defeat," Panathinaikos goalkeeper Tzorvas added. "We have to play better, try and perform and get our first win against Nigeria."
For Greece, the most disappointing aspect of South Korea's deserved victory was that both goals came from defensive errors. Despite apparent recriminations on the pitch during the game, Tzorvas said the squad were united.
"The goals we conceded were the result of mistakes, everybody makes mistakes," he said. "We made the mistakes as a team, not as individuals."
Greece play Nigeria, who lost 1-0 to an impressive Argentina in their Group B opener on Saturday, in Bloemfontein on Thursday.
