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Arsenal had bright periods prior to falling behind, but failed to test the gloves of Danijel Subasic on enough occasions to trouble to Croatian shot-shopper.
The Gunners enjoyed more opportunities after the interval and a neat passing move in the opening minutes saw Jack Wilshere hit a close-range drive that Subasic did well to keep out.
On the hour mark, Alexis Sanchez was given his first sight of goal, but the Chilean attacker sent his shot trickling wide of target.
Arsenal thought they had a penalty when substitute Gedion Zelalem sprung the offside trap before being tripped by Subasic.
The majority of those inside the Emirates thought a penalty had been given by Martin Atkinson, but instead a free kick was awarded on the advice of the referee's assistant and Subasic escaped with a yellow card, although replays show that the challenge did occur inside the Monaco area.
In the end, the Gunners were frustrated in their efforts and their defeat saw Valencia lift the Emirates Cup by virtue of their 3-1 victory over Benfica earlier on Sunday.