Former Rangers loanee Martin, 38, saluted "man of conviction" Postecoglou as he shot down heavy criticism levelled at the ex-Celtic boss.
Spurs manager Postecoglou, 59, has taken stick in recent weeks over a sticky spell of form for the Premier League club.
His side claimed a 1-1 draw with Rangers in the Europa League in midweek but that failed to end major scrutiny over his position in North London with the club 11th in the league and on a five-match winless run.
Southampton manager Russel Martin giving an incredible defence of Tottenham boss Ange Postecoglou… 👏🥹
I just hope Daniel Levy is watching…👀 #THFC #COYS 🤍💙❤️🩹 #SOUTOTpic.twitter.com/rmMdH7qkVZ
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Martin, though, believes Postecoglou has done an incredible job and reckons it's all down to his uncompromising football values, insisting it would be "crazy" to rip up his ethos.
"I see a man, when I watch his team play, a man with conviction and belief and values that he won't compromise on, which I admire a lot," said Martin of Postecoglou.
"And ultimately, it has got him managing in the Premier League and managing in the Champions League at Celtic.
"So I think he has done an incredible job, had an incredible managerial career so I have a lot of admiration and respect for him."
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Ahead of the visit of Spurs to face his Southampton side, Martin added: "I think it's really interesting because every manager that sits behind a team has some form of beliefs and some form of value system and what they deem as acceptable or what they want to see, what they won't compromise on, what non-negotiables are.
"But the ones who are only criticised are a little bit different from the norm.
"If we all believed the same thing I think it would be pretty boring. But it would be less open to criticism.
"I think hi8s team is brave, it is aggressive, they have been really unfortunate with injuries.
"It's so similar to Graham Potter when he went in at Chelsea. Everything he got praise for and credit for at Brighton, he then got criticised for at Chelsea.
"He went from being calm, studious, really brave in his approach at Brighton to then managing a team with a different expectation and then all of a sudden he didn't show enough passion on the sideline and was too emotionally consistent and all this nonsense.
"It's exactly the same with Ange. I watched a lot of his Celtic team, they were brilliant, got so much praise for being so aggressive, so brave, relentless restarts, energy, energy, energy.
"Did a great job, won lots of trophies, played in the Champions League, he goes to Spurs starts so well. When results are goof no one questions the style or his conviction or belief system.
"And then the minute it starts faltering, it's always down to that. But if you believe in something and ti has taken you a certain way in life, on a certain pathway and journey then to deviate too far from that, I think, is crazy.
"We're also, I'm pretty sure, I can't speak for him, we are adapting. We adapt shape, we adapt personnel with the same consistency and what's really important for us with the same concept of the game.
"We can't deviate too far from that otherwise we become nothing really. I don't know, I think everyone is quick to criticise these days and I have a lot of respect for him."