Sections of the travelling support booed the German national anthem prior to England’s 1-0 defeat and then sang offensive songs which referenced the First and Second World Wars.
The Football Association, English football’s governing body, are now reviewing video footage with the UK Football Policing Unit to identify those involved.
Members of the England Supporters Travel Club who took part will be banned from the group and potentially handed a Football Banning Order, preventing them from attending future matches.
On Thursday, the FA chairman Greg Clarke condemned the behaviour of some England supporters as “inappropriate, disrespectful and disappointing.”
"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.
"We are working with the England Supporters Travel Club and speaking with the Football Supporters’ Federation to come together to address this issue.
“Everyone involved in the game has a responsibility to ensure that attending a football match is a safe and enjoyable experience for all.”
The Football Supporters’ Federation, which is part-funded by the FA, echoed Clarke’s sentiments in their condemnation of the anti-social behaviour.
A spokesperson for the organisation said: “Over the last 20 years English football fans have built a worldwide reputation for our passionate support and the vocal backing we give to our teams.
“England's travelling support is made of people of all ages from a range of clubs, many of whom have worked hard in recent years to improve our standing abroad and have expressed concern to us about these chants.
“We don't want to regress to a situation where our reputation is tarnished by the actions of a minority.”