Ten-man Arsenal beat Everton 3-1 on Sunday to complete their Premier League campaign with a fifth successive win but there was no last-day reprieve for their top-four hopes.

First-half goals by Hector Bellerin and Alexis Sanchez and a stoppage-time effort by Aaron Ramsey sealed the win but Liverpool and Manchester City also romped to victories to leave Arsenal fifth, their lowest finish since Arsene Wenger arrived to take charge in 1996.

Arsenal will be missing from the Champions League for the first time in 20 years next season and although this campaign could yet end with a third FA Cup triumph in four seasons there was a sense of unrest around the Emirates.

Bellerin put Arsenal ahead after eight minutes from close range after Danny Welbeck missed his kick.

Laurent Koscielny was sent off for a reckless tackle on Enner Valencia -- a rush of blood that will rule him out of the FA Cup final against Chelsea -- but Everton were not in the mood to try and capitalise.

The marking was non-existent as Sanchez made it 2-0 from Welbeck's pass with his 24th league goal of the season in the 27th minute.

At that stage, with Liverpool being held at home by Middlesbrough, it looked as though Arsenal could yet squeeze into the top four but as news filtered through that Liverpool had gone ahead, those hopes faded.

The second half was notable mainly for chants against the club's largest shareholder Stan Kroenke by fans who have also voiced their frustration at Wenger this season.

Romelu Lukaku halved the deficit with a penalty, his 25th league goal of the season, but Arsenal hung on and Ramsey struck with a superb curler with seconds remaining.

Arsenal finished in fifth place with 75 points, four more than they managed last year as runner-up.

Everton finished in seventh spot.