About 3,500 England supporters travelled to the Greek capital for the sold-out fixture but some complained of being “pushed” and receiving “heavy-handed” treatment from local police.
The FSA said Uefa, European football’s governing body, has also been informed.
BBC Sport has contacted Uefa for comment.
One fan, Mark, wrote on X, external the treatment was “completely unnecessary” but added “unfortunately you come to expect it following England”.
Another user said, external local officers were “funnelling hundreds of fans (including children) into a few entrances” then became aggressive when “there was a squeeze”.
“Despite being told how things would operate in advance, to see the exact opposite occur in some cases, and 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,” Free Lions wrote on X.
“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.”
