Gareth Southgate has called on England's fans to support their country "in the right way at all times" after distasteful chanting was heard during the friendly in Germany.
Lukas Podolski's superb strike secured the hosts a 1-0 win against England on Wednesday.
After the German national anthem was booed, songs referencing the First and Second World Wars were audible, mostly in the first half -- something Southgate was asked about at his postmatch news conference.
"To be honest, I didn't hear what was said but it has been mentioned to me," he said.
"Obviously our travelling support in terms of number and the way they back the team is brilliant.
"We would encourage them to do that in the right way at all times."
The Football Supporters' Federation condemned the chants, with a spokesperson saying: "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.
"Unfortunately, little of the wit and imagination that goes into our club football songs is reflected at England games.
"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 that reputation is tarnished by the actions of a minority."