The superhero movie made its debut with a red carpet event on Wednesday. It was attended by actor Henry Cavill, who plays Superman in the film, reports contactmusic.com.
However, Crowe, who plays the role of biological father of Superman, reached out to his fans via microblogging website Twitter and apologised for the no-show.
He said that he has started working on his latest film project, "The Water Diviner", which will mark his directorial debut.
"I'm sorry I'm not in Tokyo for the 'Man of Steel' premiere. I love Japan. Started on 'The Water Diviner' and need every minute of preparation... Yes, directing myself, unless I don't cast me or I am unavailable due to a prior commitment... the directing one," read his tweet.