A section of the travelling supporters jeered the German national anthem and chanted songs about the Second World War.
According to the BBC, FA chairman Greg Clarke criticised the behaviour and if video footage singles out the fans responsible, they could be banned.
"The FA has consistently urged supporters to show respect and not to chant songs that could be regarded as insulting to others," Clarke said.
"Individuals who engage in such behaviour do not represent the overwhelming majority of England fans nor the values and identity we should aspire to as a football nation."
England supporters have overcome a reputation for trouble in recent years but were involved in a number of incidents during last summer's European Championships.
Clarke said the FA would crack down hard on anyone found guilty of wrong-doing.
"We are working with the England Supporters Travel Club and speaking with the Football Supporters' Federation to come together to address this issue," he said.
"Everyone involved in the game has a responsibility to ensure that attending a football match is a safe and enjoyable experience for all.
Photo: AFP English football fans during their World Cup friendly against Germany.