The Australian, 57, was forced to replace Cristian Romero with Davinson Sanchez in the 14th minute of their 2-2 draw with Brentford on Sunday.
It came after Romero had gone down moments earlier following a head clash.
And the swap was meant to go down as a concussion substitution – which would have seen Postecoglou retain his five changes for the remainder of the game.
But it ended up as one of his five subs because of Spurs‘ admin error.
Speaking after the match, Postecoglou said: “The disappointing thing is that apparently, we filled out the wrong form for a concussion sub. That is madness in this day and age.
“It is pretty clear why we took the guy off.
“It is black and white for us, we’re not going to take any risks with our people when we know what the repercussions are.
“He seems fine but the player is not the one who knows these things.”
Life under Postecoglou began with an entertaining draw at the Gtech Community Stadium.
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Following Harry Kane’s departure on Saturday, Spurs took an early lead when new signing James Maddison‘s free-kick was headed in by Romero.
Bryan Mbeumo levelled from the penalty spot after Son Heung-min fouled Mathias Jensen, before Yoane Wissa put the hosts in front.
Emerson Royal equalised in added time at the end of the first half with an impressive strike.
And that’s how things ended as Spurs now prepare for their first home game of the campaign at home to Manchester United next Saturday.