Gunners boss Arsene Wenger is understood to have been annoyed Wilshere played 90 minutes of last month's friendly against Brazil.
Hodgson said: "Wilshere is injured and that is unfortunate. We are disappointed he isn't with us because, on merit, he'd be picked and would play.
" It would have been nice if he was here, but he isn't.
"We concentrate on those who are here, and I think we've got a lot of very good players in midfield and we'll play with them.
"The thing about club managers is they've got another job to do. That conflict is always going to be there, between club and national team, because people will want them to be there playing for them.
"But I don't have any criticisms of them."