22-year old Hart is loan at St Andrews from Manchester City and McLeish, who is keen to sign him on an extension, says his England chance is surely just around the corner.
"It is up to Fabio Capello. Joe will probably be disappointed he didn't feature but Capello is a top coach and I don't think anyone can question his decisions," McLeish said. "Joe is only 22, he is young, and Fabio will probably go for experience in the World Cup.
"The jump to international level is enormous and one little error for any player and you are scrutinised to massive levels.
"It is early days for Joe but his progress is fantastic. He should be proud of that. He doesn't have to be too disappointed about not featuring with England at the moment. I am sure his time will come."