Capello resigned following a meeting with Football Association chiefs at Wembley Stadium.
Arsenal midfielder Wilshere, 20, won his first cap under Capello against Hungary in August 2010 and said on Twitter: "Shocked about news on Fabio Capello...gutted to be honest, gave me my 1st cap and believed in me! Thank you Mr Capello! #GreatManager."
Former England defender Danny Mills criticised the FA for their handling of the situation and claimed the Euro 2012 campaign will be compromised as a result.
"It think the FA have handled this very badly," he told Radio Five Live. "He's obviously decided enough's enough and walked out. He's almost dropped England right in it.
"There's an awful lot of preparation that has gone in it (Euro 2012). It just causes disruption. There will be speculation that people don't need.
"Players will be asked about Capello, the new manager and about John Terry. He's justified in his decision. Do England need this leading into a major tournament?"
Mills was also sceptical about whether Tottenham boss Harry Redknapp, the favourite to take over the reins, would be able to juggle the England job with his duties at Spurs.
"I presume Harry Redknapp is the favourite, but he's got a job to do with Spurs until the end of the season," he said. "The FA have handled this really badly. You have to find a man very quickly. Someone who wants the job.
"If it's going to be Harry Redknapp are Spurs going to allow it? The FA are almost going to be held to ransom. The Euros is going to be a trial for whoever takes charge."