Arsenal are not the sort of team that need a helping hand but Swansea City were more than happy to oblige on an afternoon when Paul Clement saw with his own eyes just how big a job he has taken on. The Swansea head coach’s first official league game in charge ended in humiliating fashion as Arsenal, aided by two own goals and an assist from Wayne Routledge, cantered to an emphatic victory in almost comical fashion.

Not everyone in an Arsenal shirt was smiling, though. Alexis Sánchez had a face like thunder when the substitutes’ board went up 11 minutes from time with his number on it. Arsenal were 4-0 ahead at the time, the game was in effect over and Arsène Wenger wanted to give Danny Welbeck a run-out as well as let Sánchez have a breather.

Except Sánchez, who had scored Arsenal’s fourth goal, never saw it that way. He looked thoroughly fed up as he walked past Wenger, took his gloves off, kicked them up in the air and pulled a coat over his head to cover his eyes.

Clement, in the opposite dugout, must have felt like doing the same in the second half. Competitive up until the interval and unfortunate to go behind to Olivier Giroud’s fifth goal in five matches, Swansea totally lost their way after the restart as it turned into an exercise in damage limitation for the Premier League’s bottom club.

Jack Cork was the first Swansea player to put through his own net, inadvertently deflecting Alex Iwobi’s shot over the head of Lukasz Fabianski. Kyle Naughton then followed suit, this time from Iwobi’s cross, and it summed up Swansea’s day when Routledge put the ball on a plate for Sánchez to volley home and complete the rout.

Sánchez has now scored or assisted 31 goals in his last 32 Premier League appearances and remains Arsenal’s most influential player by a distance, yet it was the Chile international’s actions off the pitch, rather than his contribution on it, that provided the main talking point afterwards.

“I rested him for two weeks, gave him a little breather. I think he benefited from that. I gave him another rest for today, so he will benefit from that as well,” Wenger said, with a twinkle in his eye and a wry smile.

“He’s hugely influential. When you look at the numbers, he’s been involved in so many goals. But I think, as well, we have players on the bench who are strikers who need competition, we were 4-0 up, he’s just come back from a good rest, [Mesut] Özil as well comes back from sickness, so it was a good opportunity not to be stupid.

“All the players are frustrated when they come off, some show it, some not. I’m long enough in the job to know that. I just make the decision I feel is right, that’s it. He’s a good guy who gives a lot and who always wants to do well for the team. There’s no problem. Looking at the game tonight, that’s really minor, minor, minor.”

Wenger went on to offer some kind words about Swansea and suggested that they “still have the quality to get out of it”‚ yet Clement was honest enough to admit that this performance had reinforced his views about the amount of work the club needs to do in the transfer window. Two more new faces are on their way, with Tom Carroll set to join from Tottenham for £4.5m and Martin Olsson arriving from Norwich for £5m, and others are likely to follow before the end of the month.

The one frustration for Clement here was that Mike Jones, the referee, booked Ki Sung-yeung for diving just before the interval rather than pointing to the penalty spot as Laurent Koscielny dangled a leg and the Swansea midfielder tumbled over. “When I spoke to Ki at half-time he said there was contact,” Clement said. “I got the opportunity to look back on it from all the different angles – obviously the referee doesn’t get that – and saw the reaction of Koscielny, and it’s a penalty”.

Giroud had given Arsenal the lead seven minutes earlier, turning home from close range after Özil’s header, from Sánchez’s cross, bounced off Alfie Mawson and into his path.

Although Cork was unlucky to deflect Iwobi’s shot over Fabianski early in the second half, Arsenal’s second goal had been coming amid a spell of sustained pressure. Naughton’s own goal ended any faint hopes of a Swansea comeback before Sánchez turned the screw with a fourth. Next up for Swansea is a trip to Anfield.