Declan Rice said “silly mistakes” and “naivety” is hurting Arsenal’s title challenge after the Gunners were reduced to 10 men for the third time this season in the 2-0 defeat at Bournemouth.

William Saliba was sent off for the first time in his career after he dragged down forward Evanilson near the halfway line and was ruled to have denied an obvious goal-scoring opportunity as the last man.

Rice was sent off himself in the 1-1 draw against Brighton and Leandro Trossard was dismissed in the 2-2 at Manchester City, both for game-delaying offences, but MIkel Arteta’s side were unable to avoid a first defeat of the campaign at the Vitality Stadium.

Arteta said Saliba’s red card, which came in the first half, made it “impossible” for Arsenal and Rice lamented that the Gunners had “kicked ourselves in the foot” again in the Premier League.

Following Saliba’s red card, Gabriel Martinelli had a golden chance to put Arsenal ahead but the forward was denied by Kepa Arrizabalaga before a clincal finish from Ryan Christie and a Justin Kluivert penalty wrapped up victory for the hosts.

"We’ve kicked ourselves in the foot three times in eight games and we got away with it at home to Brighton and away at Manchester City. Bournemouth kept probing and made it 2-0,” Rice told Sky Sports.

"I’m proud of the players for fighting, even with 10 men, but the naivety, we need to stop making mistakes because you want 11 players for 90 minutes and that’s what wins you football matches.

"With 10 men we showed a lot of character and personality to stay in the game. The big chance was Martinelli’s and the keeper read it and made a great save and one minute later, normally a routine we are so strong at, has done us.

"We can’t make silly mistakes. You need all your best players on the pitch at all times. The belief is so high and we will stick together. This is football, whatever happens the most important thing is that you stick together and stay in the right direction."

Saliba will be suspended for next week’s home match against Liverpool as Bukayo Saka joined captain Martin Odegaard on the injury list after picking up a hamstring problem while away with England.

Rice said Arsenal couldn’t afford to keep getting key players suspended with the club’s problems with injuries while Arteta did not comment on the decision to send off Saliba. He did add that Arsenal would not appeal the red card.

"We are obviously very disappointed with the result and gutted because we have to play another game in that context. With 10 men for 60, 65 minutes at this level, it’s just impossible,” Arteta said.

"It was a decision [the red card] made on the pitch. That decision was changed. Now I don’t think the decision is going to change again. So, decision made.

"Willy has never done anything like this but he doesn’t do it on purpose. It happens. We have to accept it, move on, and have that pain we are feeling for Tuesday.”

An uneventful opening 20 minutes saw the Gunners limited creatively by Bournemouth’s disciplined high press, the closest either side came to a goal when Raya gifted the ball with a dreadful pass only for Antoine Semenyo to thrash at the chance.

The shape of the game shifted with the sending off in the 30th minute. Evanilson still had the whole of the Arsenal half to traverse in pursuit of a looped ball over the top but crucially had manoeuvred goal side of Saliba and threatened to race clear.

Saliba was the last man - there was little chance of Ben White making up the distance to cover from right-back - and clearly dragged Evanilson to the ground, though it took a pitch-side review to convert Robert Jones’ initial yellow card to a red.

Arsenal might have defied their predicament and gone ahead had Mikel Merino not dragged wide from Marcos Senesi’s poor defensive header.

Arteta sacrificed Raheem Sterling for defensive reinforcement in the shape of Jakub Kiwior, and thereafter Bournemouth penned Arenal back.

Raya gifted them a chance when he fumbled Semenyo’s low cross then immediately saved a certain goal, springing up in a blur to smother Marcus Tavernier’s rebound.

Semenyo blew a golden opportunity to make hay on Bournemouth’s advantage at the start of the second half, ballooning over after Milos Kerkez picked him out in space at the far post.

Martinelli was sent on in attack, an affirmation of Arteta’s belief his side could nick it. Indeed they might have but for Kepa Arrizabalaga’s fine save with his legs from the Brazilian after initially giving the ball away with a casual pass.

It capped Arsenal’s best spell since the red card but soon they were rocked by Christie’s rocket, blasted in first time from a corner past a static Raya as Kluivert’s clever flick fooled the visitors’ defence.

Not long after, Arsenal’s fate was sealed. Kiwior carelessly allowed Evanilson to nip in over his shoulder, Raya raced out to repair the damage but in his haste toppled the striker. Kluivert sent the goalkeeper the wrong way from the spot for 2-0.

Includes reporting from PA