Burnham questioned how the FA had allowed the FA Cup semi-final 23 years ago to be played in a ground without a valid safety certificate, and said negligence was to blame. An initial FA statement did not contain an apology but, following calls from Hillsborough families, four hours later FA chairman David Bernstein made "a full and unreserved apology".
Burnham, who did much to have the inquiry into the disaster reopened when he was a member of the Labour Cabinet in 2009, told Sky News: "The FA need to ask themselves some serious questions."
It came after the Hillsborough Independent Panel report showed the ground was unsafe and did not have a valid safety certificate at the time of the match on April 15 1989. It also revealed a police cover-up had taken place which had intended to shift blame for the disaster, which claimed the lives of 96 Liverpool fans, to the victims themselves.
Burnham added: "The main one (question) is why did they allow a semi-final to be played at a ground without a valid safety certificate? I don't think there's an answer that people can accept because I think it was because of negligence of people's safety.
"Why were supporters allowed to go into those unsafe conditions and did the FA know of those other near misses at other semi-finals such as 1981 Wolves v Spurs and 1987 involving Leeds.
"I remember going to Hillsborough the year before and having one of the most distressing experiences of my life. All of these things were known about Hillsborough, how did nobody in football act upon them."
Hillsborough families welcomed the FA's apology to all those affected by the disaster - but said it should have been made years ago. Margaret Aspinall of the Hillsborough families support group said the FA apology was long overdue.
She told the Press Association: "We welcome the apology but the one thing that makes me angry is that we have had to wait for this report to come out before we get all the apologies that should have been made a long time ago.
"The FA did have a role in what happened so it's right we should hear from them."