Mourinho has come under fire for his part in Real Madrid's 2-0 defeat to Barcelona last week in the first leg of their Champions League semi-final, with the former Chelsea and Inter boss adopting a defensive approach at the Bernabeu and then making explosive comments to the press after the game.
UEFA has opened disciplinary proceedings against both clubs, but Switzerland boss Hitzfeld suggested the first-leg victory for Barca was justice for the sport after the way he approached the game.
"Luckily, Mourinho's destructive tactics, aimed solely at provoking and destroying the opponents' gameplan, did not work," he told German magazine Kicker.
"Such a way of playing does not relate to the demands of Real. It's really shameful for Real Madrid. It harms the good name and image of this legendary club.
"I've met him at UEFA meetings and his behaviour is faithful to his image: arrogant, haughty, chewing gum and somewhat of a boor. Barca should make him pay on the pitch."
Hitzfeld won the Champions League with Borussia Dortmund in 1997 and Bayern Munich in 2001, and has also won the Bundesliga on seven occasions as a coach.