Nobody should interpret one fine goal against limited Championship opposition as proof that Armando Broja has a place in Chelsea’s great rebuild. When the talk turns to the club’s financial fair play position, it is always pointed out that money received for academy products goes down as pure profit. Accountancy matters and Chelsea are still thinking about sharpening their attack with a new striker this month.

But supporters want to see homegrown talents thrive, even after a splurge of more than £1bn in the transfer market. Conor Gallagher, another whose future is up in the air, was given a hero’s reception when he came on towards the end of this 4-0 win over Preston North End. It makes sense to have Mauricio Pochettino developing all these young talents. It was interesting to hear Chelsea’s manager say Broja has to smile more after the forward scored his second goal of a stop-start campaign.

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The next few weeks could be crucial for Broja. Such a handful when he is fit and confident, this is the quick and powerful 22-year-old’s chance to establish himself at Chelsea. Broja, who has been searching for consistency since returning from a serious knee injury, has to step up while Nicolas Jackson is at the Africa Cup of Nations.

Puncturing Preston’s resistance with a header that Didier Drogba would have been proud of was a good start. Broja remains raw, perhaps even a little tentative for a target man, and he should have finished this game with a hat-trick.

Still, as Pochettino said, this was a moment for happiness. It was Broja who seized the initiative when Chelsea, who started slowly before charging into the fourth round of the FA Cup, were looking for the breakthrough early in the second half.

“It was important for him,” Pochettino said. “But I need to be honest, he needs to use this type of game to improve – not only his fitness or work ethic but also his body language. He needs to smile more and be more positive. This is the way he is going to improve his game.

“We are talking about one of the young strikers here in England or Europe with the most potential. He needs to push himself and we are going to help him to realise he is aggressive enough. He suffered a big injury. He needs time. But our expectation is massive.”

Pochettino is striving to improve standards at Chelsea. Asked about Cole Palmer’s assist for Thiago Silva’s header taking the playmaker to 15 goal involvements since joining from Manchester City last summer, he responded by saying he was a “little bit disappointed” with Palmer for missing an easy chance during a tepid first half.

Not having European football means Chelsea should take the cup competitions seriously this season. As a manager who is yet to win silverware in English football, Pochettino was not in a position to rotate too heavily. His selection was strong, even with Christopher Nkunku absent with a minor niggle.

Preston, 14th in the Championship, were up against it. They made a committed start and their 3-5-1-1 shape was difficult to break down at first. “The performance was fantastic,” Preston’s manager, Ryan Lowe, said. “I’m disappointed with the first goal. But the lads were excellent. They gave their all.”

Chelsea were wasteful during the first half. Raheem Sterling had two efforts saved by Preston’s goalkeeper, Freddie Woodman. Enzo Fernández, who needs to add goals to his game, missed a simple header. The Argentinian looked relieved when he rounded off the scoring during the dying stages.

The story had been one of sterile Chelsea dominance. More urgency made the difference in the second half. Mykhailo Mudryk’s role in the breakthrough typified the shift in attitude. The winger chased down a loose ball on the left and played it back to Malo Gusto, who crossed for Broja to glance a beautiful header past Woodman.

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Broja’s oomph lifted the tension. Silva made it 2-0 after replacing Alfie Gilchrist, who made his full debut at right-back. Sterling added a third with a wonderful, dipping free-kick. Fernández finished from close range. Chelsea will have a spring in their step when they visit Middlesbrough for the first leg of their Carabao Cup semi-final.