The 56 year old took up the position two years ago after replacing Marcelo Biesla.
"It is over, the chapter is closed," said Pekerman, who won three world Under 20 titles as coach and named each of his dogs after them: Qatar, Malaysia and Argentina.
"I am not going to carry on. I can leave with my head held up high. I have always believed in the players and they have not let me down.
"They have always done what was necessary to attain their objective, to the last penalty."
German assistant coach Joachim Low paid tribute to Pekerman and his policy of promoting youth.
"Pekerman is really a class act, he's an exceptional coach who has brought forward so many young talents from youth level to turn them into world class performers. He has put in years of work.
"I can't comment on his tactics today or the decision to leave Messi on the bench - we were even happier to see Javier Saviola benched also. But they had plenty of other aces up their sleeve and of course they had to replace the goalkeeper, which maybe altered their gameplan a little."