If Scott Parker was seeking some solace on the south coast after Fulham succumbed to relegation earlier this week, it didn’t arrive at St. Mary’s. Southampton swept to a comfortable victory – their margin established by Che Adams’ first half strike and a first Saints goal for Nathan Tella seconds after coming off the bench – that emphasised the size of the rebuild required in west London this summer as the Championship beckons. Even the silver lining of a first senior goal for talented teenager Fabio Carvalho, which briefly threatened an unlucky comeback, was swiftly followed by a strike from substitute Theo Walcott to put clear water between the sides once again.

Parker’s caustic comments following relegation – and his assertion in a pre-match press conference that he had yet to speak with the club’s ownership – suggested that his own future is still to be resolved. Fulham have plenty of business to take care of behind the scenes, but the absence of a genuine striker from the start, with Aleksandar Mitrovic and Josh Maja left on the bench, meant this side had an experimental look. In truth, with both sides have little to play for, this resembled a low-key pre-season friendly – and there was very little quality in front of goal in a turgid first half.

Referee Craig Pawson seemed to enter into the charitable spirit, ignoring a succession of hefty tackles before eventually cautioning Joachim Andersen for a clumsy foul near to the by-line on Stuart Armstrong. That allowed James Ward-Prowse to whip in one of his dangerous set pieces and Fulham’s defending from the free-kick was shambolic. Adams didn’t need to do anything special to lose Ola Aina, who had one of his poorest games in a Fulham shirt, and sweep a half volley into the net from six yards out.

Ward-Prowse was then denied a trademark free-kick goal, with Alphonse Areola making a magnificent save and, right at the end of the half, Danny Ings almost doubled Saints’ lead. The forward latched onto a precise pass from Takumi Minamino, kept his feet to round the goalkeeper but his cross-cum-shot was headed clear by Joachim Andersen. Fulham’s brightest moments came from Carvalho, whose energy around the penalty area kept the home defence occupied, but his shot after a clever backheel from Ivan Cavaleiro lacked the power necessary to beat Alex McCarthy.

The second half followed a similar pattern. Fulham saw plenty of possession, but as so often during this campaign, couldn’t find enough penetration in the final third. Ralph Hassenhuttl’s side didn’t have that problem and might have been further in front shortly after the interval only for Areola to deny Nathan Redmond after the winger had cut in dangerously from the left flank. You felt a second goal wasn’t long in coming and it arrived after a slick move that followed Bobby Decordova-Reid giving the ball away and saw a purposeful run from Armstrong find Kyle Walker-Peters down the right and the full-back’s low cross put a simple finish on a plate for the recently introduced Tella.

A few brave blocks prevented Fulham from getting a foothold in the contest. Decordova-Reid produced a gorgeous pass to unlock the Southampton defence only for Jack Stephens to deny Cavaleiro and Salisu arrived just in the nick of time to close down Decordova-Reid when he went through on goal. Joe Bryan drilled an effort wide from long range, but Fulham’s likeliest source of goal still looked like Carvalho, who had been switched to a number ten role in the second period.

The Lisbon-born England youth international had sparkled on a couple of senior substitute appearances earlier in the season after stellar displays for Fulham’s under 18 and under 23 sides and he lit up his first Premier League start with a smartly taken goal in the 75th minute. Having began the move around the halfway line, Carvalho surged away from Stevens to reach Decordova-Reid’s through ball and fired high into the net. Having scored on his debut for Fulham’s under 16s, under 18s and under 23s, perhaps we should have expected this precocious talent to find a way to mark this auspicious occasion, but it was still a special moment.

Any hope of a stirring comeback quickly evaporated when Walcott grabbed a third with eight minutes left. It was too easy for Southampton to play through the remnants of the away side’s defence – Armstrong’s probing ball brought the lively Tella into play and the youngster unselfishly laid it off from a shooting position for Walcott, with an untimely deflection off the unfortunate Bryan leaving Areola with no chance. Carvalho’s cameo might have been pleasing but there can be no getting away from the fact that Fulham have exited the top flight with a whimper at odds with all their fighting talk.

SOUTHAMPTON (4-4-2): McCarthy; Walker-Peters, Salisu, Stephens, Vestergaard; Ward-Prowse, Armstrong (Diallo 78), Minamino (Walcott 76), Redmond; Ings (Tella 58), Adams. Subs (not used): Forster, Ferry, Ramsay, Djenepo, Obafemi, N’Lundulu.

GOALS: Adams (27), Tella (60), Walcott (82).

FULHAM (3-4-2-1): Areola; Tete, Andersen, Adarabioyo; Decordova-Reid, Cavaleiro, Aina (Bryan 62), Reed; Anguissa (Lookman 63), Onomah; Carvalho. Subs (not used): Rodak, Hector, Odoi, Ream, Loftus-Cheek, Mitrovic.

BOOKED: Andersen.

GOAL: Carvalho (75).

REFEREE: Craig Pawson (South Yorkshire)

VIDEO ASSISTANT REFEREE: David Coote (Nottinghamshire).