The race was won by Ballabriggs, trained by Donald McCain, but the horse was too exhausted to be ridden to the winner's enclosure.
Dooneys Gate and Ornais suffered fatal injuries.
"When horses are killed at the Grand National meeting, their deaths are not accidents but entirely predictable," Animal Aid director Andrew Tyler said.
"The public has been conned into believing that the Grand National is a great sporting spectacle when, in reality, it is straightforward animal abuse that is on a par with Spanish bullfighting.
"This race should have no future in a civilised country," he said.
Tyler also had harsh words of the broadcaster BBC, accusing it of "all but concealing news of the deaths".
"In fact, one of its commentary team described the dead horses as they lay on the course as 'obstacles' - which was particularly disgusting and callous."
Ornais broke his neck and Dooneys Gate broke his back during the four and a half mile event run on a sweltering day.
In all, 20 horses have died on the Grand National course since 2000.
As in previous years, horses somersaulted and crashed to the ground, landing on their heads, necks and backs, the group said.
It noted that several horses were pulled up and Animal Aid said it was concerned about whether any of those had suffered serious injuries that could result in their subsequent destruction.
The field bypassed two jumps on the second circuit of the track, including the notorious Becher's Brook, because of stricken horses in their path.
Ballabriggs' time of 9min 1sec was nearly 14 seconds outside the course record held since 1990 by Mr Frisk, but was the second-fastest National run.
In all, 10 horses fell and four unseated their riders. Two were brought down by other horses during falls, and five horses were pulled up by their mounts.
The course has undergone major modifications in recent years to tackle welfare concerns, but they have failed to placate animal welfare advocates concerned at the toll exacted by the race.
The British RSPCA has worked with Aintree officials to introduce various changes to the course in recent years, including adjustments to the fence cores, padded jump protection and additional run-outs for riderless horses. These changes are ongoing.
RSPCA equine consultant David Muir, commenting before the race, said the death of a horse at any race meeting was never justifiable and it was crucial that, wherever possible, steps were taken to reduce the likelihood of that occurring.
"The Grand National is the most testing of races and due to the number of runners, the distance of the race and the number and variety of obstacles there is a higher risk to horses," Muir said.
"Many improvements have been made to the course including fences such as Becher's Brook; however the drop jump element of such obstacles will always be an area of concern to us."
On Thursday, Inventor was destroyed after breaking a leg in a hurdle race at the three-day Aintree meeting.