Hitzfeld was the favourite to be appointed after Euro 2004, at which point he had just ended a successful spell at Bayern Munich that brought four Bundesliga titles and a UEFA Champions League crown.
However, after holding talks with the DFB, Hitzfeld opted not to take the job due to 'exhaustion'.
"After six years with Bayern, I was on the brink of burnout," he told Welt am Sonntag.
Hitzfeld, who subsequently took a two-and-a-half-year break from the game, also revealed he had lost his passion for the game towards the end of his first stint with Bayern, which came to an end on the back of a trophy-less 2003/04 campaign.
He added: "I was only thinking, 'At least you haven't lost' whenever we won. Joy, adrenaline and motivation are so important in performance sport so I could tell something was not right with me.
"I simply would not have been capable of taking on this challenge [of coaching Germany]. I had no energy, and when your health is not fine, you can't perform to your best."
After returning to the game by retaking the reins at Bayern for 18 months, Hitzfeld - who has recently retired - spent six years in charge of Switzerland.
