Two fences were bypassed on the second circuit because of the fall by Ornais at the fourth jump and Dooneys Gate at the sixth, the notorious Becher's Brook.
"We are desperately sad at the accidents during the running of the Grand National," Thick said, "and our thoughts go out to the connections of Ornais and Dooneys Gate.
"When a horse gets hurt, everyone is deeply upset.
"Safety is the first priority for the organisers of the Grand National meeting and we will redouble our efforts to make sure that everyone involved in the event - the horses, the jockeys, the spectators - is able to participate in safety and comfort.
"Horse racing is a very carefully regulated and monitored sport.
"All horses and riders in the Grand National have to meet very high standards set by an independent panel of experts. The Grand National is a well-organised and professional race.
"Only the best horses and the best jockeys are allowed to enter and all horses are inspected by the vet when they arrive at Aintree to ensure that they are fit to race."
More than 150 specialist staff were completely focused on making the race as safe as possible, he said.
"Now that the meeting is finished, we will, as always, be looking at all aspects of this year's race to see how we can make the event safer in the future.
"We work closely with animal welfare organisations, such as the RSPCA and World Horse Welfare, to make sure we are up to date with the latest thinking and research regarding welfare and safety.
"Our job is to make sure that the horses are looked after properly and that the race is run as safely as possible."