Arsenal moved to within four points of Manchester United and Chelsea at the top of the Barclays Premier League last night with as cavalier and convincing a performance as they have produced all season. Sadly for them, despite this most comprehensive of demolitions of an already-doomed Derby County at Pride Park, the table is illusory. Only the wildest optimist or those of a certifiable nature can imagine United or Chelsea capitulating over the last two matches.

Arsenal will almost certainly have to settle for an unrewarding third place — at least victory took that out of the reach of Liverpool — and have to qualify for the Champions League next season.

Where did it all go wrong? Not in the first half of the campaign, when Arsène Wenger’s young side, dismissed by the preseason pundits, led the way from mid-September to Boxing Day, and then from late January to mid-March, before the wheels came off spectacularly.

A spate of injuries to key personnel, loss of form and lack of belief combined to contrive a sequence of only two wins in 13 matches in all competitions. Arsenal slid out of the FA Cup and the Champions League and, finally, out of contention in the Premier League. For a third successive year, they will win nothing.

Wenger wore the look of a nearly man, a “what might have been?” mood having enveloped him since that dire 13-game run took root. “Yes, we had that difficult patch in March and we paid for it,” he said after the match. “No one expected us to do well at the start of the season and, when we were under pressure in March, we didn’t have the experience to stay there.

“But we will cope with it next time. We will learn from it, of course. It was not as if our performances were that bad. We were just missing that fraction that can go for you sometimes. But we have 77 points and we won the championship with 78 \. Even when we knew the title had gone, we still love to play the game we love.”

Arsenal did play that game, after a sluggish opening, and scintillatingly so. Derby will win few plaudits, but could set plenty of records: fewest wins in Premier League history, fewest points, worst goal difference. The list goes on. At least they have kept going in the face of overwhelming adversity.

Derby had begun brightly, yet much of it was due to the uncertainty of Lukasz Fabianski, the Poland goalkeeper, who was making his league debut for Arsenal. First, he miscommunicated with Alexandre Song; then, he flapped at a corner from Eddie Lewis; then his poor clearance led to Lewis touching an effort narrowly wide.

Still, with Derby, promising starts often fade and implosion is rarely far away. “It got silly in the second half,” Paul Jewell, their manager, said. “To be honest, 6-2 flattered us. But we had put so much effort in in the first half, we were out on our feet after that.”

The goals rained in and it was the sixth time that Derby had conceded five or more this season. Nicklas Bendtner set Arsenal on their way, taking advantage of Darren Moore’s error, but Derby equalised when Jay McEveley capitalised on more Fabianski hesitancy. Robin van Persie regained the lead before half-time.

Then Arsenal got to work. Emmanuel Adebayor, on for Van Persie, made it 3-1 from close range and, after Robert Earnshaw had given Derby brief hope, the dam burst. Theo Walcott waltzed through, then Adebayor scored twice to complete 30 goals for the season and his second hat-trick against Derby. Champagne stuff again from Arsenal, but, sadly, no cigar.