The Three Lions played in the Olympic Stadium in Athens in the penultimate match of their League B Group 2 campaign.
Fans who had travelled to attend the match endured a horrendous time as they made their way into the 75,000 capacity stadium with one supporter claiming that fans were teargassed.
The supporter also claimed that tickets were not checked at the stadium's perimeter, with exit gates being opened as tensions grew.
A number of fans were still making their way into the stadium as the game kicked off at 8pm.
"We are aware that some of our fans had a difficult experience outside the ground and are obtaining more information on exactly what happened," the FA said.
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A witness told talkSPORT: "Incredulous how bad the organisation has been tonight.
"Our tickets not checked at second perimeter and could have photocopied them to get through first.
"Exit gate opened as tensions grew and game kicked off. Shambolic. UEFA need calling out on this s*** guys."
This account was supported by numerous posts on social media.
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One fan wrote: "F****** disgrace getting to the stadium. Police went mental tear gassed and battered England fans. Wife fell over barrier trying to get out of way. Deliberate policy by the Greek police."
A second said: "The Greek police are an absolute disgrace tear gassing innocent people trying to queue but as always, England fans will get the blame."
Meanwhile a third wrote: "An absolute f****** disgrace getting into this ground. Tear gassed and ambushed against fences for no fucking reason. Yet England fans are always the problem."
A fourth also wrote: "Riot police tear-gassing and t******g any England fan that moved on the way into the ground."
A UEFA Spokesperson told talkSPORT that it was a matter for the local authorities.
Meanwhile the Football Supporters' Association were extremely critical of local police.
"To see the treatment of our fans by local police using shields and tear gas to do something as simple as rearrange a queue, is so incredibly frustrating."
"On a night where we had a great result on the pitch, there is still clearly so much needed to do off it to ensure our supporters aren't put in unjustifiably dangerous situations."
"Unfortunately, once again, we are having to ask England supporters to send in their witness accounts to ourselves regarding the situation outside of the Athens Olympic Stadium," the FSA said.
The horrendous conditions endured by fans outside of the stadium were followed by difficult conditions for Lee Carsley's side on the pitch.
A green laser pen was being shone from inside the stadium into the eyes of the England players during the match.
Meanwhile, England fans were instructed to remain in their seats following the end of the match.
It's proved to be a successful night on the pitch with England racing to a 3-0 win.
They took the lead on seven minutes when Ollie Watkins netted from close range after Noni Madueke side-stepped Kostas Tsimikas and laid the ball on a plate for the Aston Villa forward.
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England went 2-0 up on 77 minutes when Jude Bellingham's low shot came back off the post and rebounded off Greece goalkeeper Odysseas Vlachodimos before trickling into the net.
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And debutante Curtis Jones extended England's advantage with a cheeky back heel past Vlachodimos.