Postecoglou announced his resignation last Tuesday, just days after securing Australia’s spot at the 2018 World Cup, confirming he would not be at the helm when the Socceroos head to Russia.
Sainsbury admitted the players were blind-sighted by his decision describing the moment they found out as "like a break up over text".
"There was always a few inklings that he was going to leave the job, but it never really hit home at the time," Sainsbury said in an interview with website 20FOUR.
"We always thought he was going to stick around and see it through and then all of a sudden word come out through the media which was a bit disappointing.
"It was sort of like a break up over text, or finding out through somebody else.
"He’s taken us on this journey and he’s done such a fantastic job, he’ left such a legacy winning the 2015 Asian Cup, qualifying the way he wanted us to qualify and I think the belief that in the squad now will carry on for the next generation.
"But I think the boys were looking forward to having him there and taking us to the World Cup in Russia."
Despite his disappointment the 24-year-old, who plays his club football with Chinese side Jiangsu Suning, praised Postecoglou and the impact he had on him personally and the team.
Sainsbury made his national team debut in 2014 under Postecoglou after missing the Brazil World Cup that year due to injury.
He was central to Australia's qualification to the 2018 tournament, and was the Socceroos' best player at the Confederations Cup.
No defender played more often under Postecoglou than Sainsbury, which could explain the former Central Coast Mariner's despair.
"I feel let down. Everyone’s got their own decision to make. We don’t know his side of the story , I don’t know if we ever will," he said.
"But my personal feeling is that I feel let down.
"I wouldn’t say he’s like a father figure but, he was one of the most positive coaches I’ve ever had and one of the most passionate.
"When you have that it hurts when they leave because you know you may not ever get that again."
FFA is currently engaged in a search for Postecoglou's replacement.
Sainsbury strongly endorsed his former Central Coast Mariners mentor Graham Arnold, the favourite to win the Socceroos job.
Sainsbury, who won the A-League championship with the Mariners in 2013 under Arnold and is in a relationship with Arnold's daughter Elissa, acknowledged the likely perception of bias.
But strongly encouraged the governing body to choose an Australian manager for the role
"People will probably say I’m biased if I said Graham Arnold," he said.
"But I think if they go Aussie they have to go for the long term option and give them this World Cup and the next World Cup and even maybe the Asian Cup after that.
"But if they go international it would just be for the World Cup. I don’t think they should take it through to the Asian Cup.
"Why give this experience to a foreign coach when you can give it an Aussie for them to have that experience and put it on their CV and hopefully build that Aussie coach up.
"So my preference would definitely be an Australian coach "