Ozil, 29, is one of a group of senior players slammed for their woeful performances at the World Cup as Germany finished bottom of their group in Russia.
The Arsenal midfielder refused to comment about a controversial meeting on the eve of the finals with Turkey president Recep Tayyip Erdogan which sparked questions about his loyalty to Germany.
Bierhoff admits it was a mistake to allow Ozil to maintain his silence as the controversy cast a shadow over the German camp.
"We have never compelled players in the German national team to do something, but always tried to convince them when it comes to certain things," Bierhoff, Germany's team director, told Friday's edition of Die Welt newspaper.
"We did not succeed with Mesut. And in that respect one would have had to consider whether to refrain from playing him."
However, in a television interview later Friday, Bierhoff backtracked.
"First of all, I'm sorry, I was wrong," he told ZDF.
"We will not put any players in the stocks like that."
Bierhoff admitted that he and three German football association (DFB) officials had approved the quotes to Die Welt.
The embarrassing public relations own-goal is the latest example of the clumsy handling of the Erdogan scandal by the DFB.
Ozil and Ilkay Gundogan, who both have Turkish roots, were booed by German fans in pre-World cup friendlies after posing for pictures with Erdogan.
Manchester City midfielder Gundogan presented him with a signed club shirt on which he had written "to my president".
Gundogan denied the meeting was politically motivated, but Ozil refused to comment.
He was the only member of the 23-man squad allowed to miss a media day at Germany's pre-World Cup camp.
Bierhoff says the issue should have been handled better.
"They fact that Mesut and Ilkay took the pictures did not bother the team so much, but the debate went on and, in retrospect, I would have tried to deal with this issue more decisively," Bierhoff admitted in the Welt interview.
Ozil was slammed on social media for woeful World Cup displays in the shock group stage defeats to Mexico and South Korea having been dropped for the last-gasp win over Sweden.
There is no doubt Ozil, who has made 92 appearances for Germany, could be one of a number of 2014 World Cup winners who have played their last international.
On Tuesday, Loew confirmed that he will remain as Germany's head coach and Bierhoff also ruled out resigning on Friday.
However, as effectively the number two in the Germany setup, he anticipates "profound changes" after the dismal campaign in Russia for which he said the entire squad should take "collective responsibility".
Bierhoff says Germany's management know they "gambled away credit" and have "registered" that fans feel alienated from the team. He said the team management take that feeling of alienation "very seriously".
Bierhoff says Loew will "sort out and reorganise everything. He will question everything, including our style of play. And then the question will arise as to which players we need."