The delegation included just three players from the national team – captain Philipp Lahm and Polish-born veterans Miroslav Klose and Lukas Podolski – as well as head coach Joachim Löw, team manager Oliver Bierhoff and DFB president Wolfgang Niersbach.
But Graumann, speaking on Sunday at the community day of the Central Council in Hamburg, accused Bierhoff of "colossal insensitivity and tastelessness." He condemned the failure to organise a visit by the whole squad, as the England team has done.
According to Monday's edition of Die Welt newspaper, Bierhoff, a former international player whose current role involves overseeing the team's public relations, rationalised the small size of the visiting party as an effort to avoid a media circus.
The DFB was keen for Friday's visit to remain low-key, with the footballing group instructed not to speak to the press, instead leaving a short note in the museum's visitors book. "For football too Auschwitz represents both a silent tribute and, above all, an obligation to speak," they wrote.
But this effort to downplay the tribute angered Graumann, who lamented a missed chance to "reach out to hundreds of thousands of young people." Particular scorn was reserved for Bierhoff, who Graumann said was guilty of "untold damage."
The controversy is merely the latest episode in a long dispute between Graumann and the DFB.
The Euro 2012 tournament in Poland and Ukraine, which begins on Friday, is the first edition of the continental showpiece to be held in eastern Europe, and has provoked uncomfortable questions for the German football hierarchy over how best to acknowledge the country's troubled history.
In March Graumann said the DFB would "send a deadly signal to the world" if the German visit to Poland and Ukraine passed without a public act of remembrance.
This angered Bierhoff, who felt that Graumann's decision to publicly air his grievances had denied the German team the opportunity to be seen to make their own decisions.
"A visit was already under consideration," he retorted. "Of course we will deal with the topic of the Holocaust with the players, whether it be through a lecture or a Kamingespräch (fireside chat)."
That disagreement led Graumann to interpret the modest delegation as an act of "brutal retaliation" by Bierhoff against his earlier criticisms. He also condemned the use of the term Kamingespräch as "intolerable," saying it evoked memories of the giant crematoria used at the concentration camp.
As well as Germany and England, the teams from the Netherlands and Italy are also planning to visit the memorial at Auschwitz during the tournament. The latter three teams are all based in Krakow, 50 kilometres from the modern-day town of Oswiecim, which Auschwitz is named after.
The German football team was not the only sporting institution to attract Graumann's ire during his Sunday address. He also reproached the International Olympic Committee, who recently announced that there would be no minute's silence during the opening ceremony of the London Games for the Israeli athetes murdered during the Munich Olympics 40 years ago.