Last year's race was also overshadowed by the death of two horses, while this year Synchronised and According To Pete had to be put down following falls.
The fatalities have led to fresh protests from animal rights campaigners, who claim the race is too dangerous.
RSPCA chief Grant has now criticised the jockey's overuse of the whip during the final stages of the race and called for the decision to be reversed.
"The death of two horses at the Grand National, bringing the total to three at the Aintree meeting, is totally unacceptable," said Grant.
"This is the second year running that two horses have died. In its current format, the risks to horses are not appropriate and we want an urgent examination of the Grand National, including a number of fences including Beecher's Brook where horses are continuing to die despite safety improvements.
"It would appear the whip was overused in the final stages of the race. If that is the case it is totally unacceptable and given the narrow margin of the win I believe the result should be reversed."
The race was eventually won by Neptune Collonges in the closest ever finish.