Antonio Conte began the afternoon in highly animated mode and, for a while, turned almost hysterically agitated in his technical area before his body language finally morphed into sulky acceptance.

As the clock ticked down Chelsea’s manager became increasingly static as he stood arms folded, expression disconsolate, on the touchline. Maybe his players were saving themselves for the FA Cup final but they never looked remotely like a side who kicked off harbouring outside hopes of a top‑four place.

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Ultimately Liverpool’s demolition of Brighton ensured Chelsea were destined to finish fifth but a performance when they were dominated by Newcastle’s outstanding Jonjo Shelvey, Mo Diamé and Ayoze Pérez was hardly what their manager will have wanted on what is expected to be his final Premier League match in charge of London’s most politicised club.

Conte said later that he was the “last person” to answer questions about Chelsea’s future. He did, though, take his players to task for their attitude and application here and warned them to up their game for the meeting with Manchester United at Wembley.

“We now have six days to change our desire, our will to fight because, if we play a game like this in the FA Cup final we do not have a chance,” he said. “There was big frustration for me because I wanted to finish the season in the best possible way. Newcastle showed great desire and fight and outplayed us but we didn’t play a good game.”

When asked whether the Cup final would represent his last game in charge of Chelsea he started laughing. “Do you think so, you have the news?” a smiling Conte inquired of his questioner before offering a riddle of a reply. “The club know very well the situation,” he said. “After Saturday we go on vacation, so we will see next season.”

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Rafael Benítez and Newcastle are also no strangers to playing politics and the manager’s future here is far from certain. But Benítez, as he continues contract negotiations with Mike Ashley, cannot have failed to be swayed by the choruses of “We want you to stay,” that echoed evocatively to the St James’ Park rafters.

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“It was pretty much the perfect Sunday for me,” said the Spaniard, who will not extend a contract entering its final year unless he receives assurances as to transfer budget and infrastructure. With suitors circling things are at a delicate stage.

“We’ve finished 10th,” Benítez said. “But 10th is not high enough for this club. The potential to do much better is there. We have to be sure we share the same ambitions. We need a squad capable of going anywhere and winning.”

Ashley later said Benítez had his “full support” and added: “I will continue to ensure that every penny generated by the club is available to him. I hope very much that Rafa will remain at Newcastle United.”

For protracted periods Newcastle looked as if they were the side pursuing Champions League qualification, piling so much pressure on their visitors that Chelsea frequently struggled to escape their own half.

With the intensity of the home side ferocious and the decibel level ear-splitting, Conte’s team were in near total disarray with the lesser spotted Ross Barkley, making a rare start, struggling to get anywhere near the ball in midfield. Part of that was down to the fact that Shelvey, like Diamé, was irrepressible. Thibaut Courtois was swiftly required to repel Shelvey’s vicious long-range half-volley and Diamé’s angled shot.

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As Shelvey revelled in making N’Golo Kanté look thoroughly ordinary he appeared every inch an England international. The consensus is that Gareth Southgate has opted against including him in the World Cup squad he is due to name on Wednesday but Shelvey has not entirely abandoned hope of a summons. Maybe, just maybe, England’s manager still has a big decision to make.

Newcastle’s playmaker helped create all three goals. The first originated with a pass that picked out the impressive Matt Ritchie, who confounded Conte’s defence with a left-foot cross from the right. When Jacob Murphy attempted somewhat audaciously to lob Courtois the goalkeeper palmed the ball clear – but only as far as Dwight Gayle, who headed into the unguarded net.

As Conte appeared in danger of physical implosion Benítez remained an oasis of serenity, celebrating the goal by giving his glasses a polish before summoning his captain, Jamaal Lascelles, for a detailed tactical discussion.

Facebook Twitter Pinterest Antonio Conte watched in fury as his players blew any chance of a top-four place with a humiliating defeat. Photograph: Scott Heppell/Reuters

With only near misses from Shelvey and Pérez and another fine Courtois save to deny Gayle ensuring the scoreline remained 1-0, that homily seemed to have the desired effect.

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Although Eden Hazard belatedly began imposing a little of his talent on the second half, it was simply not Chelsea’s day. Despite a backpedalling Martin Dubravka performing acrobatic wonders to claw Olivier Giroud’s accomplished backheel to safety following Hazard’s cross, Newcastle responded by scoring a second.

Again it was created by Shelvey, whose volleyed connection with a half-cleared cross would probably have flown past Courtois had Pérez not flicked out a boot to apply the final touch.

After Dubravka excelled in keeping a Barkley effort out with his legs, Pérez soon scored his second. This time Shelvey whipped a free-kick in and Florian Lejeune’s slide-rule pass prefaced the Spaniard dispatching a shot past Courtois from six yards.

As the manager who led Chelsea to Europa League glory Benítez never felt an iota of love at Stamford Bridge. He is smothered in the stuff on Tyneside but is determined not to let his head rule his heart. “We’ll see how the conversations [with the board] develop,” he said. “We’re still talking, maybe even tonight, so we’ll see what happens.”