The Frenchman has long been implored to spend money on big-name players and, after more criticism had been directed his way, he said he was still looking to do so.
A tricky week awaits the Gunners with a Champions League qualifier against Fenerbahce ahead of them, but Wilshere - while sympathising with the fans - has asked them to stand firm.
"Tough to take! Feel the fans frustration but trust me we are giving our all! Must forget today now and focus on Wednesday night!" he wrote on Twitter.
"Massive game for us, will be tough in turkey but we must be resilient and brave! Thanks for your support as always!"
Christian Benteke scored twice for Villa after Olivier Giroud had put the home side ahead. Laurent Koscielny was also sent off on a miserable afternoon, capped when Antonio Luna put the seal on the visitors' win.
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