Hitzfeld, who won the Champions League with Bayern in 2001, praised Rangnick for addressing his problems last week and can understand his fellow coach's position having struggled with similar issues himself.
"I was under a great deal of pressure in 2004," the Switzerland boss told Sky television.
"I had been released by Bayern and a week later, Franz Beckenbauer called me in his role with the German football association and told me I was going to be the new Germany coach.
"I told him I could not do it. I was exhausted and needed a break.
"He could hardly understand it and said that it is not as stressful a job as in the Bundesliga, or as Bayern coach, and that I could do it.
"It was difficult time since the media had also built up a lot of pressure. I believe that was a difficult but courageous decision from me at the time to turn down Germany."
With that in mind, Hitzfeld added: "I have the greatest respect for Ralf Rangnick, that he had the courage to say that he no longer had the strength to motivate the team and that he wanted to step back.
"It takes a lot of courage to be able to admit that to yourself and then go public with it."