Spurs utterly dominated the opening period at the King Power Stadium against Leicester City, playing bright adventurous football with attacking fullbacks and flowing moves as they penned their newly-promoted opponents back.
But they only managed one goal to show for their superiority, scored by right back Pedro Porro.
That left them vulnerable, and they paid for a familiar defensive lapse when veteran Jamie Vardy was allowed to poach an equaliser with the Foxes' first effort on target.
Postecoglou, currently Australia's most high-profile soccer export, made a positive impression in his opening campaign, but the pressure is always on in the Premier League and he needs to build on it with a top-four finish.
Ange Postecoglou looks less than impressed as Tottenham throw away victory at Leicester City. (AP PHOTO)
This year he has more of his own squad and apart from Yves Bissouma had a full group to choose from.
The Mali midfielder was dropped after posting on social media a video of himself inhaling nitrous oxide, possession of which is illegal in England.
Postecoglou could include club record signing Dominic Solanke, a Stg 65m ($A125 million) recruit from Bournemouth, who started up front alongside Brennan Johnson and Heung-min Son.
Leicester were unable to call on their biggest pre-season signing, midfielder Oliver Skipp, who had left Spurs as part of Postecoglou's squad-trimming earlier in the day for an initial Stg 20m ($A39 million).
Worries about financial fair play regulations mean City have barely strengthened since promotion and new manager Steve Cooper, previously at Nottingham Forest, led the line with former England striker Vardy, now 37.
He was a spectator for much of the opening half as former Foxes teammate James Maddison dictated play.
Porro's goal highlighted Tottenham's attacking approach. Though playing right-back he was advanced throughout and shortly before the half hour ghosted late into the box to head in a cross from Maddison, who had been given too much time by an opposition who ought have known better.
James Maddison finds Pedro Porro with a delightful ball and Tottenham have their first goal of the season �— Optus Sport (@OptusSport) WATCH 📲 https://t.co/JZlp4G7hg3 pic.twitter.com/nT1NhCBDveAugust 19, 2024
By that stage Solanke should have opened his Spurs account. Nevertheless, a second Tottenham goal seemed sure to come. Then shortly before the hour, with Christian Romero drawn towards the ball, an unmarked Vardy neatly headed in an unexpected equaliser from Abdul Fatawu's cross.
Postecoglou made a quadruple substitution, then a double change, but Spurs could not regain their mastery.
As it was, both sides could have won with City's Wilfried Ndidi and Tottenham sub Richarlison both going close in the final minutes.
Rodrigo Bentancur had to leave the pitch on a stretcher during the second half but was reported to be conscious and doing well.
9°C