There have been performances like these over the years that have seen Chelsea managers, no matter how successful, dethroned by the Russian who once ran this club with little room for sentiment, so one wonders how the new regime of American private equity might be different for Thomas Tuchel.

Different bosses; same fixation on results; and the sense that something is malfunctioning at the heart of Chelsea. This was a sensational performance from Dinamo Zagreb, who exploited the flaws in Tuchel’s team with a sense of purpose that was thrilling to watch.

Yet as Chelsea’s Champions League-winning manager switched between formations and personnel it was notable that he just kept coming up with the same results.

The winning goal was scored by Mislav Orsic, an occasional Croatia international who scored a hat-trick against Tottenham Hotspur in the Europa League last year and another against West Ham in the same competition last December. At 29 he has played in Italy, South Korea and China, and against Chelsea he looked more dangerous than all the many expensive attacking options at Tuchel’s disposal.

It felt like a game too early for the debutant Pierre-Emerick Aubemeyang wearing that mask to protect a jaw injured in a home invasion suffered less than a week earlier in Spain. Yet what will alarm the giant consortium of money that now owns Chelsea is just how mediocre their great collections of big names looked against some comparatively less famous players in the home blue shirts.

Indeed, if Chelsea’s new principal co-owner Todd Boehly runs those names through his scouting database he will find that the likes of Josip Misic, Bruno Petkovic and Robert Ljubicic are valued at considerably less than those whom he has bought this summer. This was Dinamo’s night but it also said something about Chelsea too.

As the clock ticked down and Tuchel tried in vain to change the course of a team that had fallen behind in the 13th minute, the Chelsea manager and his assistant Zsolt Low were both booked for complaining about time-wasting. Their true unhappiness, however, seemed to lie with the team they were trying to coax a performance from.

Later Tuchel would make the distinction that his criticism of his players were statements of good faith – simply describing what he saw – and for that his honesty must be commended. It will be for Boehly and others to decide where that leaves his manager’s relationship with his squad.

Defeat was the third in a row away from Stamford Bridge for Tuchel, a new landmark in a troubled start to the season. Later he would say that he never saw it coming – “I was in the wrong movie” he observed, with that feel for the right phrase in a bad moment.

He worked his way through the old complaints: a lack of hunger and a lack of intensity from his players. In Los Angeles and wherever else the titans of private equity convene perhaps they will wonder if they too have seen this movie before.

This was a chastening night for the two expensively acquired centre-halves Kalidou Koulibaly and Wesley Fofana who were at different times out-muscled and out-paced by the electric Dinamo front pair of Orsic and Petkovic. Playing as a classic combination of pace and power, these two forwards, with low-key careers across the football globe, cut Chelsea open for the goal.

The sight of £70 million Fofana trailing a distant second behind Orsic will be one that lives with the new ownership for some time. 

It took all of Dinamo’s key players to contribute the kind of performances they will remember for a long time – but, even so, they were outstanding. When the 27-year-old Petkovic dragged Koulibaly to the long ball struck by Ljubicic on 13 minutes from his own area, Chelsea were split in two.

The ball dropped in behind and suddenly Orsic had five yards on Fofana. We waited for the Frenchman to turn on the jets – but he never recovered. Whether it was the arc of the run or the fear of the foul, or both, Fofana did not get close to Orsic who used the angle of his body to clip his finish right-footed over Kepa Arrizabalaga.

The Dinamo coach Ante Cacic, a 68-year-old on his 24th managerial appointment and his second at this club, said that his team had simply played to their strengths.

“When it is raining you have to wear a raincoat and when it is winter you have to get your feet warm,” he said. “We had to do everything to make them play slower. To be a well-organised opponent against their quality and not give them the opportunity to come near our goal.”

They did so with fine performances in midfield from Misic and Luka Ivanusec and a general sense of purpose that grew the longer that Chelsea’s muddle continued. At half-time Tuchel swapped a 3-4-3 system for a 4-4-2. Off came Cesar Azpilicueta, formerly on the right side of the defensive line, and in his place, if not his position, came Hakim Ziyech on the left side. It meant that Raheem Sterling found himself in a central midfield role.

When Marc Cucurella later came on for Ben Chilwell, the defensive line would change again and Fofana would find himself on the right side of a three, reinstated for the latter stages of the second half. For all the times they had the ball at their feet, Chelsea barely created a chance worthy of the mention until Reece James hit the post with a late shot.

The closest to another Dinamo goal was a beautiful drive from the right wing-back, the Macedonian Stefan Ristovski which Arrizabalaga did well to touch onto the bar. Every Chelsea cross flung into the box was headed out. Saturday’s visit to Fulham is looking more daunting than it did just a few days previous.

• A Telegraph report