The Italian had previously stated he was "a fascist but not a racist" - and his appointment led to former foreign minister David Miliband to resign as Sunderland vice-chairman.
After several days of controversy with even the Dean of Durham expressing his disquiet, Di Canio issued a statement saying he does not support the ideology of fascism.
Bernstein said he hoped a line could now be drawn under the controversy.
The FA chairman told reporters at the Soccerex conference in Manchester: "Paolo di Canio certainly appears to have retracted some of his previous statements and there have been some moves in the right direction.
"I think it is really a matter for Sunderland and their chairman and their board and Paolo Di Canio.
"We deplore any association with fascism and any association with racism but hopefully Paolo Di Canio is moving the agenda in the right direction and that issue will be put to bed."
Newcastle fans have been warned by police not to taunt Di Canio with fascist salutes when the north-east rivals meet on Sunday at St James' Park.