Southgate has called for calm ahead of England's Nations League match against Germany on Tuesday.
The Football Association is reportedly on high alert for crowd trouble in Munich, given the rivalry between the two teams and the fact it is the first big away game for England supporters since 2019 because of the coronavirus pandemic.
England's last trip to Germany for a friendly in 2017 was overshadowed by the poor behaviour of a minority of England supporters, who booed the German national anthem and sang chants about World War Two.
Two England fans were handed lifetime bans for performing Nazi gestures at the match in Dortmund and in total, 27 members of the England Supporters Travel Club had their membership suspended for varying lengths of time.
Southgate is keen to avoid a repeat on Tuesday and has urged supporters to behave themselves.
When asked if fan trouble affects his players, Southgate replied: "It definitely has an impact.
"Staff are working on things detracting from the main part of their job, you are embarrassed when you hear about it, because you know it's a representation of your country, in the same way there's been a brilliant representation of that across the world in the last couple of days [with the Queen's Platinum Jubilee celebrations].
"So we're always conscious of that, I think we can only give the correct messages, it's then you've got to rely on people behaving themselves."
England are currently serving a two-game stadium ban as punishment for the crowd trouble which marred the Euro 2020 final against Italy at Wembley.
As a result, England's next home Nations League match, coincidentally against Italy at Molineux on Saturday, will be played behind closed doors.
Southgate acknowledged that the Wembley trouble, coupled with the recent spate of pitch invasions in English football, has brought the "spotlight" back onto England fans.
But he hopes those supporters travelling to Germany can create a positive atmosphere for the team.
"I think we know because of the landscape at the moment that the spotlight is going to be on so we all want to be coming away talking about a brilliant night and be talking about good football and a stunning atmosphere," added Southgate, speaking after Saturday's 1-0 defeat to Hungary.
"We don't have any control over that, we can only ask that's what our supporters deliver.
"For a large number it is, I think we have supporters from all parts of the country who travel brilliantly, and leave foreign countries with a great feeling about England and English supporters, we know that there's always been others that do it a different way, and that's been the same for 40-odd years, we've still got to try to police that as well as we can, and make sure we keep stopping people from doing those things.
"That's not easy to control, frankly."
Featured Image Credit: PA Images
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