The horse developed pleuropneumonia – a bacterial respiratory infection – after the race.
The infection resulted in the onset of sepsis, which is “likely to have been a key factor” in the cause of death.
Blood tests taken on the day of the race indicated that the infection had not been present in the horse on raceday.
The British Horseracing Authority (BHA) said the post-mortem is just “one part” of their reviewing process of any fatality and that Celebre D’Allen’s death will be analysed in detail.
Celebre D’Allen was a 125-1 shot at the National, which was won by jockey Patrick Mullins on Nick Rockett.
On Tuesday, it was also announced that Mullins has been given an eight-day ban after his ride was referred to the Whip Review Committee.
The amateur jockey, 35, breached the whip rules during the race, using his whip eight times after the final fence when the limit in jump racing is seven.
He will be suspended for eight separate days including 23 and 25 April.
Celebre D’Allen’s death prompted criticism from animal rights groups, with Animal Rising saying the sport of horse racing was to blame for the horse’s death.
Animal Aid said it was “disgraceful” to allow a horse of Celebre D’Allen’s age to be ridden in the “most gruelling race in the country”.
The BHA said there had been 24 13-year-old horses since 2000 who have competed in the Grand National, with no previous fatalities.