The 21-year-old midfielder is unable to represent the Three Lions for the upcoming World Cup qualifying double-header against San Marino and Montenegro due to a recent ankle injury, and is currently undergoing rehabilitation in Dubai.
Wenger was reportedly frustrated at Hodgson's decision to play Wilshere for 90 minutes of the February friendly with Brazil, but the England boss was quick to deny any conflict with the Gunners manager.
"The thing about club managers is they've got another job to do," Hodgson told reporters. "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."
He added, "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. But injuries occur. It occurred to Michael Dawson and Gary Cahill."
"These things are unfortunate but part and parcel of life as a football coach. 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."