English FA Premiership/ Bolton Wanderers 3 Arsenal 1: It was little more than a month ago that Arsene Wenger, speaking ahead of his 10th anniversary at Arsenal, described Nicolas Anelka as his "biggest find" for the club.

The Arsenal manager made another discovery here thanks to his former striker and one that will sit uncomfortably with many supporters. Anelka's first Premiership goals for Bolton prompted Wenger to concede the title race is already over for his stuttering side.

"It would be very pretentious to say we can be champions when we could be 15 points behind (after the Manchester United-Chelsea match)," said Wenger.

The Frenchman denies Arsenal are in transition but his argument appears hollow. Less than three years ago the Gunners were in the midst of a season in which they would not lose a single match, yet on Saturday Sam Allardyce, the Bolton manager, claimed there is now a blueprint for all clubs to expose Arsenal's frailties.

"They always get irate when you upset them and that is why other teams have copied what we do," said Allardyce. "You know they will lose their cool and composure and, when they do that, you know you have got a chance."

The Bolton manager could not conceal the satisfaction this victory provided. It is no secret he is not a friend of Wenger, who dislikes Bolton's uncompromising style, but the Arsenal manager will always be welcome at the Reebok Stadium. This was the third time in four seasons Bolton have defeated Arsenal at home. Wenger's side were outfought last year when Bolton won 2-0 and Allardyce employed the same tactics in the first half to prevent Arsenal, hampered by Thierry Henry's absence, finding any rhythm. Not for the first time this season, a lacklustre start led to an early concession. "It shows we are not mature enough to deal with it at the moment," said Wenger.

Rarely can the Arsenal manager have looked so tormented. He patrolled the touchline with a permanent scowl, his patience stretched by Arsenal's abject defending. Wenger pointed to the "lack of experience" in the back four but it was their most seasoned defender, Kolo Toure, who was involved in all three Bolton goals.

Toure had failed to track Abdoulaye Faye in the ninth minute, the Senegalese arrowing his run towards the near post before heading in El Hadji Diouf's corner. Moments later Kevin Davies pushed Emmanuel Eboue in the chest - his hands raised but not high enough to earn a red card following a bizarre new directive - and Arsenal reacted as Bolton had hoped: Freddie Ljungberg and Jens Lehmann were booked for dissent.

Anelka plundered a glorious second from 30 yards, the forward cutting inside Toure before spearing a swerving shot into the top corner. It was his first league goal for Bolton since arriving from Fenerbahce for £8 million in August.

Arsenal won a corner straight from the restart, Gilberto Silva stole into the penalty area unmarked to head home Cesc Fabregas's cross.

Any hopes of a fightback were dashed, though, when Ivan Campo's superb pass exposed Toure's poor positioning, allowing Anelka to angle a right-footed drive into the far corner. Allardyce was not expecting the Incredible Sulk, as he was famously nicknamed, to talk through his goals. "Because he is a quiet lad, I have to make the conversation," said the Bolton manager. "He has definitely been a bit fed up and he has been asking what we can do to get him a bit better service."

Not so many long balls would be a start although Bolton's position in the table, third and two points above Arsenal, might placate the Frenchman for the time being. There was little to soothe Wenger, the Arsenal manager seeing his side hit the woodwork three times through Ljungberg, Emmanuel Adebayor and Fabregas. When asked about his forlorn demeanour, the Arsenal manager replied: "There are a lot of men unhappier than me."

Allardyce did not enjoy a glass of wine with Wenger after the match but he made it clear there was food on offer. "(Wenger) makes disparaging remarks about us all the time - it's about time he ate some humble pie," said Allardyce.

• Guardian Service