Postecoglou’s side needed a win at Stamford Bridge to close the gap on fourth-placed Aston Villa in the race to finish in the Premier League’s top four.
But instead they slumped to a third successive loss after goals from Trevoh Chalobah and Nicolas Jackson fired Chelsea to victory over their London rivals.
Fifth-placed Tottenham are seven points behind Villa with four games left, while Unai Emery’s men have three to play.
With their Champions League hopes fading, Postecoglou conceded his players are no longer playing with the confidence that infused their performances earlier this season.
Taking the blame for Tottenham’s untimely slump, the Australian said: "It wasn’t good enough and I have to take responsibility for that, it is on me.
"I am the manager and I am the one putting them out there and it was not good enough.
"When we put in a performance like we did in the first half it meant my message wasn’t getting through."
Tottenham’s issues with defending set-pieces were decisive again, leaving former Celtic boss Postecoglou to bemoan his side’s collapse in the final weeks of his first season in charge.
"I feel like we’ve lost a bit of belief and conviction in our football and that is on me to change that," he said.
"It wasn’t about conceding the first goal, it was our approach to playing football and we were nowhere near good enough. That is on me.
"We’ve been in a bit of a grind for a while now, that is part of our challenge and part of our growth. We have to go out there and perform and sometimes you have to grind out. We were poor today."
Asked if Tottenham’s top four bid was over, the downcast Postecoglou added: "I don’t know how to answer these questions. We were poor today, what is the point of thinking about anything else?
"There’s no major formula. We will work hard and make sure we get it right. My responsibility is to make sure we play better next time."
Chelsea boss Mauricio Pochettino has masterminded two wins over his former club Tottenham this term.
But those successes have been rare bright spots in a difficult first season in charge for the Argentine.
Eighth-placed Chelsea could still salvage their campaign by qualifying for Europe, but even that is not guaranteed to save Pochettino from the club’s demanding co-owner Todd Boehly.
Boehly has already sacked Thomas Tuchel and Graham Potter since taking charge in 2022, with Pochettino responding to recent reports about his future by pleading for time to revive the club.
"Maybe today because we won I can explain a little bit better. I want to say enough is enough. I think all managers need time to translate their ideas and their philosophy. We need to have time, but it is not my decision," Pochettino said of his future.
"If we want to match the history of Chelsea I think there is a lot of work to do. We will see if we have time to build this way.
"It’s difficult to see every single week that I am under scrutiny and judgement. Yes, it’s not my decision to be here or not to be here."
ARSENAL HOPE FOR MAN CITY SLIP-UP
Arsenal resume their quest for Premier League glory against Bournemouth this weekend knowing they have no margin for error with Manchester City hot on their heels.
Mikel Arteta’s Gunners are a single point above Pep Guardiola’s men with three games left but City, who host Wolves, crucially have a game in hand.
Arsenal have hit a rich vein of form since their 2-0 defeat by Aston Villa last month, but are competing against a City side who are now unbeaten in 31 games in all competitions.
The Gunners have a chance at least to apply some pressure by beating Bournemouth in the early kick-off at the Emirates on Saturday.
Bournemouth have registered their highest-ever points tally in a Premier League season to climb to 10th spot but have only beaten Arsenal once before.
City were not at their best against Nottingham Forest last weekend but still found a way to win and are strong favourites to wrap up an unprecedented fourth straight English title.
Arsenal will cling to the hope that Wolves can complete a rare double against City after they won 2-1 at home earlier this season.
Guardiola, for his part, does not believe his side can afford to drop any points in the run-in.
"With four games left, it’s like climbing a mountain," he said. "They are very tough games... If we draw a game, we are not going to win the Premier League. It is what it is."
MAN UTD SEEK TO STOP ROT
Manchester United’s sorry season could plumb new depths unless they kick their costly habit of conceding late goals.
Erik ten Hag’s chaotic team have won just two of their past nine Premier League matches and have tricky games to come against in-form Crystal Palace, Arsenal and Newcastle, who are their closest rivals for a Europa League spot, before they face Brighton on the final day.
United have two potential routes into the Europa League, either by beating Manchester City in the FA Cup final or finishing sixth in the Premier League.
Seventh place could also be enough for UEFA Conference League football next season.
The Red Devils have never finished below seventh in the Premier League but that is far from certain to remain the case given their poor form.
West Ham and Chelsea are within striking distance but have been hampered by their own inconsistency in recent months.
BURNLEY’S ESCAPE ATTEMPT
Burnley appeared dead and buried just weeks ago but they have lost just one of their past eight league games to remain in the battle for survival.
Vincent Kompany’s team are still second from bottom of the table but are just two points from safety with three matches to play.
The first of those is at Turf Moor against Eddie Howe’s Newcastle, who have lost 10 times on the road this season.
Burnley’s final game is on May 19 against Forest, currently one place above the drop zone, and Kompany wants his team to be still alive when the teams meet.
"For us, the biggest thing is, can we give ourselves a game against Forest where we have something to look forward to?" said the Belgian.
"We don’t need much more. We just want that opportunity on that one day. That’s enough for us to rally to something special."
Forest will hope to pull away from the danger zone when they travel to already relegated Sheffield United.