Spurs narrowly missed out on the top four last season, but were expected to make a positive start to the new campaign against their newly-promoted opponents at the King Power Stadium.
It all started well for them as Pedro Porro headed Spurs into a deserved first-half lead, but the visitors squandered chance after chance and were punished when Jamie Vardy equalised for Leicester in the 57th minute.
Tottenham had several more chances to win the game, but failed to take any of them, with Richarlison missing a glorious opportunity in the dying seconds.
The Sky Sports cameras quickly turned to the touchline where Postecoglou was seen doubled over in despair, seemingly in disbelief as to how his side had failed to win the game.
Tottenham missed a host of chances, with James Maddison unable to inspire them to victory against his former club
Radio host and Arsenal super-fan Roman Kemp couldn't resist sticking the boot in as he posted a video of Postecoglou with his pained expression alongside the caption 'love football'.
Another X user was equally happy to see Tottenham slip up, as they pointed out it was only the 'first game of the season' and Spurs had already dropped points.
In the build-up to Monday's game, Postecoglou had pointed out that he tends to win silverware in his second season at a club, and one supporter was happy to remind him of his words as they mockingly wrote: 'It’s alright, he "normally wins things" in his 2nd season', alongside a laughing face emoji.
Spurs played some exhilarating football at times last season, but fell away badly in the closing stages of the campaign to miss out on the Champions League.
They have been widely tipped to kick on this year, especially after an exciting summer that has seen them bring in the likes of Dominic Solanke and Archie Gray, but some fans feel Postecoglou may already be wondering if his team will ever deliver on their potential after Monday's setback.
'What have I done to deserve this? That’s what’s on his mind,' one X user posted.
'Big Ange has had enough already,' quipped another.
Spurs were also trolled by Vardy during the game, with the veteran striker turning to the away fans to point out that he has won the Premier League while the north London club have not.
He then had an X-rated spat with Cristian Romero, who made his feelings clear on Vardy taking his time to get off the pitch when he was substituted in the second half.
Tottenham already have some catching up to do after just one match following victories for Manchester City, Arsenal, Liverpool, Manchester United, Aston Villa and Newcastle over the weekend.
They will get another chance to get their first win on the board on Saturday afternoon when they host Everton, with the Toffees also aiming to bounce back after losing 3-0 at home to Brighton in their opening game.