The Gunners fell six adrift of the Champions League places after their 1-0 defeat to north London rivals Tottenham – with Liverpool yet to play this weekend.
Harry Kane delivered the key moment at Wembley with a thumping header from Ben Davies’ cross.
Arsenal missed out on a top four place for the first time in 20 years last season to be forced into the Europa League.
The Gunners steamed through their group – having topped BATE, Cologne and Red Star Belgrade – with a round of 32 clash with Swedish minnows Ostersund on Thursday.
Manchester United burrowed their way back into the Champions League this season after winning the Europa League – with a 2-0 victory over Ajax – despite ending up sixth in the domestic league.
But Wenger insists he won’t stop hunting down league points to get back into the showpiece European competition – with eight more games in the Europa League to negotiate.
“It was a game we couldn’t afford to lose,” the Frenchman said. “It makes it more difficult now, but we have to fight.
“Manchester United decided that once they were in the semi-final. We are far from the semi-final.”
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