"The DFB, of course, respects the special situation for our players with migrant backgrounds, but football and the DFB stands for values that Mr. Erdogan does not sufficiently respect", Grindel said, as quoted by ESPN.
"That's why it's not good that global players allow themselves to be manipulated for his electoral campaign".
Ozil who plays for Arsenal and Manchester City's Gundogan met with President Erdogan who was visiting the United Kingdom for as part of an official trip in London on Sunday. "It certainly hasn't helped the DFB's integration efforts".
The meeting comes as Erdogan campaigns for re-election after calling a snap poll for June 24, bringing the vote forward by a year and a half.
"As German internationals we adhere to the values upheld by the DFB and we are aware of our responsibilities", added Gundogan.
But the images caused a furore in Germany, with lawmaker Cem Ozdemir, himself of Turkish origin, reminding the players that "the president of an global German footballer is called Frank-Walter Steinmeier", referring to the German head of state.
TFF Turkish Football Federation Vice President Servet Yardimci, a UEFA Executive Committee member, said Erdogan liked meeting soccer players but that Ozil and Gundogan were not part of the election campaign.
Turkey, under the reign of president Erdogan, have been accused for human rights violation for many times. Erdogan also said he also would be discussing regional and global issues with May. He believes the president used the stars for political stunt.
Germany team coordinator Oliver Bierhoff also expressed concern over the photos and said he would speak with the players.
"I don't think we should involve them, they are Turkish but are playing for another national team".
Speaking on Tuesday, Germany coach Joachim Low said Ozil and Gundogan - both included in his initial World Cup squad - must learn from the Erdogan controversy.
"We've always been clear that we want Turkey to uphold its global obligations, including respect for freedom of expression and political freedoms", he said.