Cklamovski became the highest-profile Australian manager currently in the Football League when hired in June by the fourth-tier club which has former Manchester United stars David Beckham, Gary Neville and Paul Scholes among their superstar backers.
Having helped Postecoglou to great success over a 15-year alliance, which featured the Socceroos' Asian Cup triumph in 2015 and a Japanese League triumph with Yokohama F. Marinos, the 47-year-old Cklamovski is now targeting silverware off his own bat after a spell as Malaysian national team boss.
But he couldn't have suffered a more deflating start to his reign as Salford were well beaten 3-1 by Barnet in their League Two opener in London, leading him to offer an apology to the travelling fans.
"It's on us because the performance wasn't where it needed to be. We're disappointed, and it's a hard one to swallow because it's not a reflection of who we are and definitely not a reflection of who we want to be," Cklamovski told Salford's in-house TV channel.
"I take responsibility for that, but we're all devastated inside, gutted.
"We apologise to the fans that travelled - that's not the team that they want to watch and that's not the team that we are, so it's got to hurt us."
Salford were two goals down at the break, after Oisin Gallagher and Charlie Lakin cashed in on defensive errors, and Kabongo Tshimanga made it three late in the game with Salford, despite an improved second-half performance, only able to earn a late consolation from Ade Oluwo.
Cklamovski will hope it's just a false start after a promising pre-season, as he seeks to emulate his old mentor.
"I've been on my own for eight years, but for 15 years I was privileged to share a journey with Ange," he told The Sun on the eve of Saturday's match.
"It's something I feel truly blessed about. We shared many great moments together from football and life, but some iconic moments for Australian football as well.
"It's a special connection for sure. He's a special man, super coach and leader who I'm blessed to have as a mentor.
"Whatever I do, I like to always reflect back and be an extension of his legacy. That's how much I love him, that's how much he means to me."
The Football League's other Australian boss, Jon Brady, who's operating in the same fourth tier with Port Vale, also got off to a losing start on Saturday (Sunday AEST) as his side went down 2-0 at Oldham Athletic, leaving him to offer some harsh words about their defeat.
