Little Josh was the latest horse to lose his life after falling and breaking his shoulder during the Topham Chase.
"We are sad to confirm that is has been necessary to humanely put down Little Josh on welfare grounds, as a result of his fall at the 15th fence in the Topham Chase," an Aintree statement said.
"He received immediate veterinary attention for a broken shoulder, but this injury was not treatable and it was the necessary course of action."
The 11-year-old horse was trained by Nigel Twiston-Davies and ridden by his son Sam and has been racing since 2006.
"He's gone out doing what he loved the most. He's jumped round those fences before and it's one of those things," said Twiston-Davies.
"It could happen anywhere. It could happen at home and it's not the fences - it could have happened at a park course.
"It's desperate, as he is one of Sam's favourite horses and he has been a great servant."
The RSPCA said in a statement that "they cannot defend such deaths but we cannot condemn the efforts made by the BHA and Aintree to try and produce more forgiving fences."
They added: "We are looking into the cause of the horse's death and awaiting post mortem results and until we have more information we will be unable to comment in detail.
"The RSPCA remains committed to working with the racing authorities to try to reduce the risks to racehorses.
Meanwhile two jockeys Liam Treadwell (on Regal D'Estruval) and Andrew Lynch (Mister First) both had to be treated for injuries after falls.
On Thursday Katie Walsh's mount Battlefront, trained by her father Ted, collapsed and died during the Fox Hunter's Chase after being pulled up at the 11th fence.
Recent deaths have prompted several changes to the Grand National course, and there will be more this year as the start has been moved forward 90 yards while timber frames in the fences have been removed.
But the changes have always seemingly been to little avail: safety improvements began in earnest after the 1989 race saw two horses killed, yet since then horses have continued to die in the race at an average of one a year.