Auckland were expected to make a quick exit from Morocco but the Oceania champions had other ideas, winning two games before stunning Cruz Azul 4-2 on penalties in the match for third place on Saturday.
The clash was decided on penalties after Cruz Azul's Joao Rojas cancelled out Ryan De Vries' first-half opener at the Stade de Marrakech.
But the Auckland amateurs were not to be denied, Sanni Issa stepping up to score the match-winning penalty as the New Zealanders became the first team from Oceania to win a medal at the Club World Cup.
"I'm the happiest man in the world because we've overcome every hurdle," Tribulietx said afterwards.
"Half of my players are amateurs but we haven't lost a single match here [Auckland were defeated in by San Lorenzo in extra time in the semi-finals].
"We deserve to finish where we have because we've been brilliant from beginning to end. I hope this performance will have a positive impact on football in New Zealand.
"We've had a few tricky moments along the way, starting with the first match against Moghreb Tetouan, which was a matter of life or death. After that we just tried to make sure we were up to the job. No one expected us to come third and it's a real honour."
Auckland made it through the tournament with three wins from four matches, ensuring they collected a staggering $3.27million in prize money.
Half of that amount will be distributed among the team, while the other half will be awarded to the other eight ASB Premiership clubs in New Zealand.
As for Cruz Azul, they had nothing but praise for the Auckland amateurs.
"I was impressed by the physical and mental strength of the Auckland City players, who've had to play one game after another," said coach Luis Fernando Tena.
"They're exceptional players and I'd be happy to have them in my team. I'd like to congratulate our opponents for taking third place because they thoroughly deserve it."