Liverpool defender Agger caught Wilshere on the foot with a heavy challenge during England's 1-0 win over Denmark on Wednesday night.
Wilshere played on for almost 50 minutes after receiving treatment for the injury, but after being cleared of any serious injury straight after the match Arsenal and England's worst fears were confirmed on Thursday when scans showed the midfielder has suffered a hairline fracture to his left foot.
Wilshere is facing up to six weeks on the sidelines meaning he is set to miss the run-in to the rest of the Premier League season and his World Cup hopes are now hanging by a thread.
"It was 50-50. You have to go for those challenges," Agger told the Daily Mirror.
"I was going for the ball and I think I got the ball, but the referee didn't."
England boss Roy Hodgson absolved Agger of any blame for the injury and admitted he felt sorry for Wilshere.
"It's always sad when you have a player come from a club, use him on international duty and he gets an injury," noted Hodgson.
"It's very sad and disappointing for Jack and Arsenal but unfortunately these things happen.
"It was an honest challenge but he took a nasty kick and I can only hope he recovers as early as possible."