Maurizio Sarri said last week that he would not enter the January market for a centre-forward but on the day Chelsea announced the capture of the attacking midfielder Christian Pulisic from Borussia Dortmund it was the team’s shortcomings at the sharp end of the formation that were placed under a harsh spotlight.

By the end of the evening Sarri was muttering about how he had nothing to do with incoming business, that it was up to the club’s board and how it knows what his opinions are. “I think we need something different in terms of characteristics,” he said with regard to his attacking options. Was this a change of heart?

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Álvaro Morata was back in the Premier League starting XI for the first time since the defeat at Wolves on 5 December, replacing the injured Olivier Giroud, but he fluffed two good chances and had another contentiously ruled out for offside while Eden Hazard was twice denied by Southampton’s 22-year-old goalkeeper Angus Gunn, who had a top-flight debut to remember.

Chelsea did not do enough as a team in a tepid and one-paced performance and their desperation was summed up in stoppage-time when Marcos Alonso went down softly under a challenge from the substitute Shane Long in a vain attempt to win a penalty. The left-back would have been better advised trying to shoot.

At full-time there were boos from the home support and Chelsea can now feel Arsenal and even Manchester United a little bit closer to them in fourth place. The cushion to Arsenal in fifth stands at three points and it is a quirk of the fixture list that Chelsea still have to visit both of the Manchester clubs, Arsenal and Liverpool.

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Chelsea are the lowest scorers in the top six by a margin and they ran aground against a Southampton team who defended as though their Premier League survival depended on it. Gunn, who joined from Manchester City last summer, showed sound positioning throughout – he left his line to tidy up on more than one occasion – while in the 19-year-old right wing-back Yan Valery the visiting side had an unexpected star. Up against Hazard, he more than held his own.

Sarri lost Willian on 37 minutes to a calf injury following a challenge with a little on it from Maya Yoshida, and he joins Pedro and Callum Hudson-Odoi on the list of injured wingers. It was the last thing Sarri needed given the paucity of creative options he had on the substitutes’ bench. He included a complete back four on it. The manager said that Pedro would return to training in one week, Giroud in 10 days.

The day was a whirr of transfer activity for Chelsea, with the headline item being the signing of Pulisic – he has been loaned back to Dortmund for the remainder of the season – but there was also a move from Monaco for Cesc Fàbregas and one from Wolves for Tammy Abraham, the striker who is currently on loan at Aston Villa.

Facebook Twitter Pinterest Cesc Fàbregas made his 500th appearance in English football and was seen waving to fans after being linked with a transfer to Monaco. Photograph: Chloe Knott - Danehouse/Getty Images

Sarri brought Fàbregas on as a 68th minute substitute for what was his 500th club appearance in English football – not the most significant landmark, perhaps, but one he wanted to reach before he departs – and at full-time he could be seen waving to the home fans. It seemed like a goodbye, although he is expected to play in Saturday’s FA Cup tie here against Nottingham Forest. Fàbregas wants to join Monaco this month and he has to hope that Chelsea can sign a replacement to help make it happen.

Southampton were compact, they crowded the ball and asked Chelsea one question: do you have the guile to break us down? They did not and it seemed as though the frustration set in early. Midway through the first half, there was audible grumbling from the home crowd.

That said, Chelsea did create three decent first-half chances, with the big one coming when Hazard took down a high ball and smacked a shot into Gunn’s face. Morata had blown a headed opportunity in the 12th minute while he saw another effort deflected wide by Valery.

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Hazard cut inside to work Gunn on 58 minutes and Morata would be denied by the tightest of offside calls following Fàbregas’s pass. Towards the end the substitute Ruben Loftus-Cheek ushered in Morata but he shot straight at Gunn, betraying his rock bottom confidence. “We played a very good match for 80 metres of the pitch,” Sarri added. “The problem was the last 20 metres.”