Last season was the first time Arsenal have failed to finish in the top four under Wenger, but Sunday's loss leaves them in sixth place, 13 points behind Tottenham in fourth.
Arsenal's next game is on Thursday, March 8th, against Milan in the Europa League-perhaps they'll be able to pull themselves together by then.
Arsenal found it hard to fight back, keeping the bulk of play in Brighton's end but not managing to get off many shots.
Twenty minutes later Brighton doubled their lead through Glenn Murray's header, although it looked as though Cech could have done more to keep the ball out.
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Speaking to BBC Sport after the win, which lifts Brighton into the top half of the division, Hughton hailed his players for showing the "ugly side" of their game.
Hector Bellerin has been dropped for Calum Chambers following the poor displays up against City winger Leroy Sane and links to Juventus, while Alex Iwobi starts in midfield.
Instead, Arsenal were repeatedly pushed back with Cech forced to save well from Gross before Dunk wastefully headed over the bar.
It is painful to admit this of someone who has been such a shining light in the Premier League but the time to say farewell appears close.
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When Arsenal finally got a foothold in the game they couldn't do anything with it.
Either way, the Czech goalkeeper hit Twitter to accept all responsibility for Arsenal's fifth loss in six matches, saying, "If you want to win a game away of home in the best league in the world your GK can't concede 2 goals like I did today ... it's simply not possible ..."
Are Arsenal better off without Cech in goal?
In the second half, Arsene Wenger side pressed further for an equaliser and had chances from Henrik Mkhitaryan, Aubameyang and Mesut Ozil.
Cech is an outstanding professional - something he showed in the second half here when, with other players seeking confrontation after an terrible Sead Kolasinac challenge flattened Ezequiel Schelotto, he ran 40 yards to check on the injured Brighton player - and an intelligent, respected voice in the dressing room but his on-pitch role is surely on borrowed time.
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