Roberto Martinez's side recorded a 4-1 victory in their final game before the World Cup, but the win was marred after Chelsea's Hazard limped off in the 70th minute.
Speaking to reporters, Thorgan, who plays for Borussia Monchengladbach, said that this brother blamed him for the injury.
"It is not the time to take risks. He had done enough in the game to be able to come off. Eden said it was my fault," the Monchengladbach man said. "When I wanted to pass to him, it fell a bit short and the defender caught his knee a little bit.
"But I don't think it is anything serious. Eden has grown in strength during the three friendlies that we've played.
"He has shown he can take the team to the top. We've seen we need Eden at his best if we are going to do anything in the tournament."
Martinez described Hazard's injury as a "dead leg" after the match.