BBC Sport’s Holly Bacon was in Gelsenkirchen as a fan and said the scene outside the ground was one of “chaos”, adding there were lots of delayed trains and “confusion over platforms”.
“There was no signage or directions and really poor lighting,” she added.
The short journey back to the city of Mulheim took Holly two and a half hours, with other supporters not arriving home until 04:00-05:00 local time after missing connections.
“Quite a few people staying in Wuppertal were unable to get back and had to fork out for taxis. Really, really poor organisation,” she said.
Andy, who had travelled with his son, said the number of fans travelling back the same way caused significant problems.
“People were walking to stations further down hoping that there might be space on the next train but no-one was getting off,” Andy told BBC Radio 5 Live.
“They didn’t want to wait for any more trains, so they just pushed further and further on. It was dangerous, it was poorly managed. There should’ve been a lot more stewarding there.”
Fellow Three Lions supporter Jamie added the situation at the final whistle was an “absolute nightmare”, saying staff “were just packing people on to the trains”.
England head to Frankfurt to face Denmark on Thursday, and then Cologne the following Tuesday to take on Slovenia in their final group game.
Concannon said the FSA will once again speak to local organisers.
“We were always confident coming to Germany that things would go well, so we hope that because of this hiccup it improves,” he said.
Meanwhile, a spokesperson for the Football Association told BBC Sport it has been notified of the concerns.
“We are aware of the issues our fans experienced in Gelsenkirchen last night and will ensure their feedback is passed on to the organisers. The FSA and Police will do this too,” said the FA.
National rail operator Deutsche Bahn told Reuters it and local operators had worked to increase train capacity.
“Football fans know that as soon as the referee blows his whistle, everyone goes home. It can get crowded on the platform,” a spokesperson told the news agency.
Meanwhile, police in Gelsenkirchen say a British national has been arrested after altercations between England and Serbia fans prior to the game.
Videos on social media showed tables, chairs and bottles thrown before riot police arrived, with seven people from Serbia also arrested.