Football Federation Australia are yet to finalise a shortlist for Postecoglou's successor, with the big kick-off against France in Kazan just over five months away.
The FFA hope to have a new man in place before March's friendly against Norway in Oslo, with Graham Arnold, Roberto Mancini, Luis Felipe Scolari and Marcelo Bielsa among the names linked.
Bristol City skipper Wright said he was disappointed at Postecoglou's exit following the 3-1 win over Honduras in Sydney, but understood his reasons.
The former Melbourne Victory and Brisbane Roar chief has since joined J-League side Yokohama F. Marinos after turning his back on the chance to lead his country at a second World Cup.
His decision left the Socceroos without a coach to attend last month's draw in Moscow and the players wondering who will be in charge when they next meet up for a friendly against Norway in Oslo on March 23.
"There was talk about it in the press but we just ignored it and got on with our jobs," Wright said.
"He was still our coach and that's what mattered at the time and we were all very surprised to see him leave."
Wright said Postecoglou gave no indication to his squad that the end was nigh after the euphoria of victory over the Central Americans at ANZ Stadium.
"After the win over Honduras he spoke to us all and told us how proud he was and there was a massive celebration," he said.
"The next day most of the boys were back on planes and flying back to their clubs so there was no meetings or discussions or anything.
"But I have complete respect for his reasons and why he's chosen to do what he has done."
Wright, a standout performer in his side's narrow 2-1 defeat to Manchester City in the first leg of the League Cup semi-final on Wednesday (AEDT), said he owes the former Socceroos boss a debt of gratitude.
As a wide-eyed 21-year-old playing for Preston in League One in 2014, Postecoglou took him to the World Cup and handed him his first international cap against Saudi Arabia later that year.
"The time with Ange was absolutely amazing and I'd have loved to see him stay," he said.
"I'm very grateful for what he has done for me and my football career. He changed my look on things and my mindset as a player.
"He took me to a World Cup, a Confederations Cup and I was part of a team that secured qualification for a World Cup.
"I know I can speak for the majority of the other lads and say he was great for us."