Oxlade-Chamberlain, capped 14 times for his country, missed Arsenal's Wembley triumph due to a groin injury, although Wenger said he was on the brink of selection.
And the 20-year-old is on track to keep his place in Roy Hodgson's 23-man squad for their group-stage campaign, and will join the England squad for their training camp in Portugal.
"He was desperate to play (at Wembley). Pain-wise he could have played," Wenger said.
"I judged him short physically. I felt that in this game we wanted to play players who were completely fit and prepared. He was a bit short physically.
"The medics said to me he could play 20 or 30 minutes but you can't program it like that. That's why I left him out. He's on the way up but he needs more fitness work now.
"But he's okay for England, yes. It was hard to leave him out. Alex and Jack Wilshere will both go to Portugal."
Oxlade-Chamberlain will fly out to join his national team-mates on Monday.
