Sammie Szmodics and Liam Delap scored before the break, with the Blues then superbly seeing out victory after Rodrigo Bentancur pulled a goal back for the home side in the 69th minute.
Speaking to Spurs TV after the game, the Australian branded the display as 'unacceptable.'
He fumed: "It’s hugely disappointing and I guess from my perspective unacceptable because we started the game nowhere near the levels we needed to be and gave ourselves a mountain to climb.
“Second half we had the ascendancy and enough opportunities to get the job done, but we didn’t do enough with it.”
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Asked about the first half, he replied: “We were just way too passive, with and without the ball.
"We allowed them to feel comfortable, which is what we don’t want to do, when we’re at home especially, but irrespectively.
“And we paid the price for that.”
The Blues proved adept at slowing the game down and seeing out the win, something which Postecoglou accepted as part of the game.
“It’s part of the Premier League now," he admitted. "Clubs are strategically doing it.
“You can almost set your clock that at 20 minutes someone will go down and they’ll go over and get instructions from the coach.
“If we want to overcome that, we’ve got to make sure that we don’t give opportunities for the opposition to get ahead in games and try and kill it, we can control that.
“But it’s up to the officials to sort of work that out.”
This defeat came after his side arrived back in the UK at 2am on Friday morning having lost 3-2 at Galatasaray in the Europa League on Thursday.
Asked if that trip to Turkey and late return was a factor, Postecoglou insisted: “No, it’s not that.
"And if it is, it’s even worse for me so… look, it’s my responsibility and I’ve got to fix it.
“We’ve been inconsistent this year, fair to say, and we shouldn’t be that inconsistent.
"And when you are that inconsistent, the responsibility lies with me to try and overcome that.”