The England international was substituted after a lackluster display on the opening day of the new Premier League season but his coach said the midfielder had been feeling unwell.
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The Gunners beat their fellow Londoners 2-1 on the opening day of the new Premier League season, with Aaron Ramsey snatching the points late.
However, Wilshere already had been withdrawn by the time of the Gunners' late winner, with Alex Oxlade-Chamberlain impressing in his place.
While Wenger conceded Wilshere had struggled to impose himself against Palace, he pointed out that there had been mitigating circumstances.
"[Wilshere] was sick in the last few days and I felt he started to still miss some competitiveness," the Frenchman told reporters. "I had options on the bench as well."
Wenger also pointed out that Wilshere should be afforded some time to build up some momentum given how much ankle trouble he has had to endure in recent seasons.
"Let's give him games," the Gunners boss implored. "For me, the most important thing for him is not to have any problem with his ankle.
"But it looks like he's on the right way on that front. He looks sharper every week at the moment."