Those lost 30 minutes will haunt Mauricio Pochettino. Chelsea’s inexplicable lethargy during extra time against Liverpool will stain their head coach’s reputation. For Pochettino, who is yet to win a trophy in English football, the accusation that he bottles the big occasions will be hard to shake off after the manner of his side’s 1-0 defeat in the Carabao Cup final.

Reputations are made in those moments. Unfortunately for Pochettino, it is hard to find anyone willing to place much store in Paris Saint-Germain’s financial might helping him to three trophies in France. Before facing Liverpool there was more focus on the semi-finals and finals that got away from the Argentinian during his Tottenham days. Unfairly or not, the only way to answer the question of whether Pochettino was ruthless enough was with a statement win. He had to show Chelsea fans he was capable of beating Jürgen Klopp.

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It was heading that way at the end of normal time. Pochettino could justifiably argue he had provided Chelsea with the tools to beat an injury-hit Liverpool inside 90 minutes. All that was missing was a finish, but it still looked like Chelsea were going to win when extra time arrived.

What happened next, though, was not a good look for anyone involved. Why did Chelsea relinquish control to Liverpool’s teenagers? Was Pochettino’s team talk the problem or was it the team? Was it because Chelsea have nobody capable of dominating a game? Or was it because Pochettino, who later spoke about a lack of on-pitch leadership and hinted at his inexperienced side hoping for penalties, was unable to affect anything from the touchline?

Whatever the answer the manager is usually most exposed. The truth is these are now dangerous times for Pochettino. Whispers are already floating out of Stamford Bridge. Pochettino, who cannot afford to lose at home to Leeds United in the fifth round of the FA Cup on Wednesday, is already under review despite only arriving last summer. Well-placed sources have predicted a split if Chelsea, who are languishing in 11th place in the Premier League, miss out on their minimum expectation – European qualification.

Yet it can be simplistic to home in on the manager. Pochettino has overseen some damaging results and there is no clear pattern to the football. Yet it is debatable whether he is Chelsea’s biggest problem given that he has contended with injuries all season, has overseen some excellent performances against top sides and, most pertinently, is not responsible for the £1bn spend on such an oddly shaped squad.

This is not Pochettino’s project. He is the head coach, the man tasked with building a winning side out of a squad with no natural goalscorer, but he was not the driving force behind buying all those young players. Todd Boehly and Clearlake Capital, Chelsea’s owners, installed a recruitment team for that. They brought in the co-sporting directors, Laurence Stewart and Paul Winstanley, and the co-director of recruitment and talent, Joe Shields. It wasn’t Pochettino’s idea to buy Axel Disasi, the centre-back who lost Virgil van Dijk for Liverpool’s winner on Sunday.

Chelsea need to look within. They need to explore why Graham Potter, who was recruited after impressing with Brighton, floundered during his seven months in charge last season. They need to question why, five years after leading Spurs into a Champions League final, Pochettino looks so uneasy. Has he really lost his magic touch? Did Potter? Did his hard-earned coaching knowledge simply disappear after joining Chelsea?

Many people think the problem is elsewhere. While Chelsea’s hierarchy remain happy with Stewart and Winstanley and want to build the foundations around them, others are less complimentary. There are questions over the quality of their signings. People struggle to see the idea behind the squad. It is noted that the best players are still mostly the academy graduates.

Some buys look promising but others have struggled. Mykhailo Mudryk, the £89m winger, has toiled and Chelsea’s feeling that they overpaid for Moisés Caicedo and Enzo Fernández must have deepened when the £220m midfield duo failed to regain the initiative against Wataru Endo, Bobby Clark and James McConnell at Wembley.

There is no escaping reality. It might not be long before Chelsea have to ask whether this model is working. There has already been the departure of Christopher Vivell, who lasted less than a year as technical director after being squeezed to the margins. Recent history suggests that nobody is ever on entirely safe ground at Stamford Bridge.

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Self-preservation could come into play. Shields is popular and is more in the background. Stewart, who is close to Winstanley, is seen as thoughtful and given to mucking in with colleagues. Winstanley, though, inspires less warmth. Previously at Brighton, he has quickly become the most prominent figure in the recruitment team. Getting close to the powerful co-controlling owner, Behdad Eghbali, has helped. Winstanley has been involved in a lot of big deals and some sources believe he is going nowhere. Others think he could be vulnerable if Eghbali’s trust wavers. Someone will have to carry the can for the iffy signings.

Whether it is Pochettino remains to be seen. Chelsea have to tread carefully. Owners who are already on to their fifth manager must consider that potential hires will be unnerved by a culture of hiring and firing, especially as the summer looks set to be competitive. A lot of big clubs will have managerial vacancies and Chelsea need to consider where would they would sit in that market if they miss out on Europe again. If they want to revamp their squad they are not going to find it so easy to sell players who were handed eight-year deals after signing for inflated fees.

Perhaps this is not the time for more upheaval. Liverpool trusted Klopp in difficult times. Arsenal stuck with Mikel Arteta. Sacking the manager is the obvious choice. Chelsea will not progress unless they give someone time to build. Pochettino has three months to convince them not to be hasty.