"It was a great result. I said in the week we expected to come here and get a result," Wilshere told the FA's official website.
"We didn't surprise ourselves. I know a few people have been saying a few things but we believed in ourselves and we showed that tonight.
"We knew the longer the second half went on at 0-0, they weren't going to be happy, the fans weren't going to be happy and we used that."
England host San Marino in their next qualifier on October 9.