Their buildup was dogged by the controversy surrounding Ozil and Gundogan after the players, who have Turkish roots, were booed in pre-World Cup friendlies for meeting Turkish President Recep Tayyip Erdogan.
German fans took a dim view of the perceived divided loyalty, by booing the pair in a friendly defeat to Austria.
"Whether that is right or wrong is another matter," added Bierhoff, who said the players did not act "maliciously", but had been "naive".
Off-field distractions aside, the Germans arrived well-prepared.
They are bringing 26 sets of jerseys among their 12 tonnes of equipment.
"There will be a high standard of opposition. Spain have improved, while Brazil and Argentina are up there."
Germany have won just one of their last six friendlies, but all the focus is on their opening game in Moscow on Sunday against Mexico.
"The first group game is always a sticking point, because it tingles," said veteran forward Thomas Mueller, who will lead Germany's attack.
The nervy 2-1 win over Saudi Arabia is now in the past.
"There is no reason to blubber now, we are world champions," added Mueller.
"We have many players who are in a fit state."
The Germans hope that particularly applies to Neuer, the world-class Bayern Munich goalkeeper who has played just two matches since fracturing his foot last September.
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