Sheffield Wednesday apologised after the report was revealed due to the fact the stadium did not have a valid safety certificate at the time of the match.
The report also showed a police cover-up had taken place, which shifted the blame elsewhere, in the incident which claimed the lives of 96 Liverpool fans.
Bernstein said in a statement: "We are deeply sorry this tragedy occurred at a venue the FA selected.
"This fixture was played in the FA's own competition, and on behalf of the Football Association I offer a full and unreserved apology and express sincere condolences to all of the families of those who lost their lives and to everyone connected to the City of Liverpool and Liverpool Football Club."This should never have happened. Nobody should lose their lives when setting out to attend a football match and it is a matter of extreme regret and sadness that it has taken so long for these findings to be published and the truth to be told.
"For 23 years the families have suffered unbearable pain and we have profound sympathy for them.
"I would like to commend the professional work of the Hillsborough Independent Panel, while also recognising the tireless commitment shown by so many people in maintaining the fight for justice, particularly the family support groups.
"The FA has co-operated fully with the Independent Panel throughout this process and has released all documentation in line with their requests. I would also like to make clear that we will of course fully co-operate with any further inquiry.
"The FA and English football has changed immeasurably, and learnt many lessons in the last 23 years. Through advancements in safety and investment in facilities English football is now a much safer, more welcoming environment for supporters."