If they can not travel to their major English rivals and win, what chance do they have at the Nou Camp or the Bernabeu where Real Madrid and Barcelona usually score for fun?
It was impressive to see Arsenal play this way, with focus, character and balance, not least because that has been so lacking from so many of their recent performances.
"We know he can be conservative away from home but he's showing the opposition too much respect by sitting deep and not attacking away from Old Trafford". Today they had their scarves out and they were singing.
"If you look overall at the goals we have conceded since we have played this system, it's quite positive overall", he added. "Of course it's a different role but so long as things are going well, why change?" That much is proved by looking at the league table. "But to beat Manchester United is double as nice".
At the other end, David De Gea pulled off an outstanding save from Aaron Ramsey, arguably Arsenal's man of the match, and also blocked a powerful shot from Alex Oxlade Chamberlain. He may prefer playing in the middle - all players do - but at wing-back he has the ideal opportunity to showcase his strengths, his athleticism and his delivery.
Xhaka, who joined Arsenal before the start of the season, has scored four goals in 41 appearances for the club in all competitions. The first half ended at 0-0.
The manager's credit column this season already contains the League Cup, with the Europa League possibly to come.
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The Switzerland global put Arsenal ahead courtesy of a deflected long-range effort before former United forward Danny Welbeck headed home a second just three minutes later. It's my style of play and nobody can make me change that.
They are now sixth with 63 points from 34 games and can close the gap with a win at Southampton on Wednesday.
Juan Mata says the Manchester United squad will "keep on trying until the last game" to finish the Premier League season in the top four.
While most Arsenal fans are preparing for a taste of Thursday night football next season in the Europa League, the Swiss midfielder is adamant his team can somehow close the gap.
After the match, Wenger said: "There is still a chance mathematically, although we need some help from others".
But when you see Arsenal play well it is impossible not to wonder why they do not do it more often.
Xhaka, 24, said: "We always have hope - hope dies last". Maybe those games have skewed expectations because when Arsenal play competently it now feels like a welcome surprise, and it certainly shouldn't.
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